{
  "title": "Constructions (Loci) - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the locus of a point at a fixed distance from a fixed point? 🔵", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Square"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "The locus of points equidistant from two fixed points is ______. 📏", "options": {"A": "circle", "B": "perpendicular bisector", "C": "angle bisector", "D": "line parallel"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Locus of a point at constant distance from a fixed line is ______. 📐", "options": {"A": "one line", "B": "two parallel lines", "C": "circle", "D": "perpendicular line"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Which tool is essential for constructing loci? 🛠️", "options": {"A": "Protractor", "B": "Compass", "C": "Set square", "D": "Ruler"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "A point moves such that it is always 3 cm from point O. Its locus is a ______. ⭕", "options": {"A": "line 3 cm long", "B": "circle radius 3 cm", "C": "square side 3 cm", "D": "triangle"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Locus of points 2 cm from a given line AB consists of ______ lines. 📈", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "The perpendicular bisector of AB is locus of points equidistant from ______. ↔️", "options": {"A": "A and origin", "B": "A and B", "C": "A and line", "D": "B and midpoint"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "A point moves keeping equal distance from two intersecting lines. Its locus is ______. ✖️", "options": {"A": "circle", "B": "two lines", "C": "angle bisector", "D": "perpendicular line"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "If a dog is tied to a pole with a rope, the locus of the dog is a ______. 🐕", "options": {"A": "line", "B": "rectangle", "C": "circle", "D": "ellipse"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "Locus of center of a rolling coin (moving in straight line) is ______. 🪙", "options": {"A": "circle", "B": "line parallel to ground", "C": "zigzag", "D": "point"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "A point moves so that its distance from x-axis is always 5. Locus is ______. 📍", "options": {"A": "y = 5", "B": "y = ±5", "C": "x = 5", "D": "x = ±5"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Locus of points equidistant from sides of an angle is ______. 📐", "options": {"A": "median", "B": "angle bisector", "C": "altitude", "D": "perpendicular bisector"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Constructing a perpendicular bisector requires ______ arcs from each end. 🔄", "options": {"A": "one", "B": "two", "C": "three", "D": "four"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "A point is always 1 cm from a circle of radius 4 cm. Locus is ______. 🔴", "options": {"A": "circle radius 5 cm", "B": "two concentric circles", "C": "circle radius 3 cm", "D": "line"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If a point's distance from (0,0) is constant, locus is ______. 🎯", "options": {"A": "line through origin", "B": "circle centered at origin", "C": "square", "D": "parabola"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Angle bisector construction uses arcs drawn from ______. ✏️", "options": {"A": "vertex", "B": "midpoint", "C": "any point", "D": "intersection"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Locus of midpoints of all chords of length 4 cm in a given circle is ______. 🎵", "options": {"A": "a circle", "B": "a line", "C": "a point", "D": "a square"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "A point moves such that it is equidistant from two parallel lines. Its locus is ______. 📏", "options": {"A": "a line between them", "B": "a circle", "C": "two lines", "D": "a rectangle"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "To construct a 60° angle, we draw an arc of radius equal to ______. 📐", "options": {"A": "side length", "B": "any radius", "C": "given length", "D": "twice side"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Locus of points at distance 3 from point A and 4 from point B could be ______. 🔵🔴", "options": {"A": "0, 1, or 2 points", "B": "a line", "C": "a circle", "D": "two circles"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Find locus of points equidistant from two intersecting lines making 70°. 📐", "options": {"A": "single line", "B": "two perpendicular lines", "C": "two lines bisecting angles", "D": "circle"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Construct triangle ABC given BC=6 cm, ∠B=45°, AB - AC = 2 cm. How many solutions? 🔺", "options": {"A": "0", "B": "1", "C": "2", "D": "infinite"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Locus of centers of circles touching two intersecting lines is ______. 🔵", "options": {"A": "two lines", "B": "angle bisectors", "C": "perpendicular bisector", "D": "circle"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "A point moves such that sum of its distances from two fixed points is constant. Locus is ______. ➕", "options": {"A": "circle", "B": "ellipse", "C": "parabola", "D": "line"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Locus of a point whose distance from point (2,3) equals its distance from x-axis is ______. 📍", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "ellipse"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "Two points A and B are 8 cm apart. Locus of point P such that PA² - PB² = 16 is ______. 🔺", "options": {"A": "circle", "B": "line ⟂ AB", "C": "line ∥ AB", "D": "perpendicular bisector"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "To construct triangle given base, base angle, and sum of other two sides, we draw ______. 🛠️", "options": {"A": "perpendicular bisector", "B": "angle bisector", "C": "arc with compass", "D": "line at given angle"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Locus of point P such that ∠APB = 90° where A,B fixed is ______. 📐", "options": {"A": "line", "B": "circle with AB as diameter", "C": "perpendicular bisector", "D": "angle bisector"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "A point moves so that it's always 5 cm from a fixed line. Locus is ______. 📏", "options": {"A": "one line 5 cm away", "B": "two lines 5 cm away", "C": "circle radius 5 cm", "D": "rectangle"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Given base BC=7 cm, ∠B=60°, AB+AC=10 cm. How many triangles possible? 🔺", "options": {"A": "0", "B": "1", "C": "2", "D": "infinite"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Locus of centers of circles passing through two fixed points is ______. 🔄", "options": {"A": "circle", "B": "perpendicular bisector", "C": "angle bisector", "D": "line parallel"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Construct a triangle with BC=5 cm, ∠B=45°, AC=4.5 cm. Possible triangles? 🤔", "options": {"A": "0", "B": "1", "C": "2", "D": "infinite"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Locus of point P such that area of ∆PAB is constant (A,B fixed) is ______. 📊", "options": {"A": "line parallel to AB", "B": "circle", "C": "perpendicular to AB", "D": "angle bisector"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "A ladder slips touching wall and floor. Locus of its midpoint is ______. 🪜", "options": {"A": "straight line", "B": "circle", "C": "ellipse", "D": "quarter circle"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "Given base BC, ∠B, and difference of other sides AB - AC, construction uses ______. 🛠️", "options": {"A": "perpendicular bisector", "B": "angle bisector", "C": "arc from B", "D": "line at angle"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Locus of point P where PA + PB = 10 cm, A,B fixed 6 cm apart is ______. ➕", "options": {"A": "line", "B": "ellipse", "C": "circle", "D": "no locus"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "A point moves keeping equal distance from two parallel lines 10 cm apart. Locus is ______. ↔️", "options": {"A": "circle", "B": "line midway", "C": "two lines", "D": "rectangle"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "To draw a triangle with given base, base angle, and altitude, we first draw ______. 📏", "options": {"A": "base", "B": "angle", "C": "perpendicular line", "D": "arc"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Locus of a point whose distance from origin is twice its distance from (3,0) is ______. 🎯", "options": {"A": "circle", "B": "line", "C": "parabola", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Two lines intersect at 50°. Locus of points 2 cm from both lines has ______ points. 🔵", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "hard", "question": "Find locus of point P such that PA² + PB² = AB², A,B fixed. 🧠", "options": {"A": "circle with AB as diameter", "B": "perpendicular bisector", "C": "line through midpoint", "D": "empty set"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "Given base BC=8 cm, ∠B=60°, and median from A=5 cm. How many triangles? 🔺", "options": {"A": "0", "B": "1", "C": "2", "D": "infinite"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "hard", "question": "Locus of point P such that ∠APB = 60° (A,B fixed) is ______. 📐", "options": {"A": "circle", "B": "arc of circle", "C": "line", "D": "two lines"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "Construct triangle given BC, ∠B, and altitude from C. Steps involve drawing ______. 🛠️", "options": {"A": "line parallel to BC", "B": "arc from B", "C": "perpendicular from B", "D": "angle at C"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "A point moves so that ratio of distances from two fixed points is constant (≠1). Locus is ______. ⚖️", "options": {"A": "line", "B": "circle", "C": "perpendicular bisector", "D": "angle bisector"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "Locus of centers of circles touching a given line at a given point is ______. 🔵", "options": {"A": "line parallel to given line", "B": "line perpendicular at point", "C": "circle", "D": "two lines"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "hard", "question": "Given base BC, ∠B, and circumradius R, construction uses ______. 🔄", "options": {"A": "perpendicular bisector of BC", "B": "arc of radius R", "C": "angle bisector", "D": "median"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Locus of point P such that PA = 2PB where A(0,0), B(6,0) is ______. 📍", "options": {"A": "circle", "B": "line", "C": "parabola", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "Triangle ABC given BC=7 cm, ∠A=60°, altitude from A=5 cm. Possible triangles? 🔺", "options": {"A": "0", "B": "1", "C": "2", "D": "infinite"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "hard", "question": "Locus of point P where PA² - PB² = k (constant), A,B fixed is ______. 📊", "options": {"A": "line ⟂ AB", "B": "line ∥ AB", "C": "circle", "D": "ellipse"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "A circle rolls along a straight line. Locus of a point on its circumference is ______. 🔄", "options": {"A": "straight line", "B": "circle", "C": "cycloid", "D": "ellipse"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "Construct triangle given BC, median from B, and altitude from C. Key step: draw ______. 🛠️", "options": {"A": "perpendicular bisector of BC", "B": "arc with radius = median", "C": "line parallel to BC", "D": "angle at B"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "hard", "question": "Locus of point P such that sum of squares of distances from vertices of square is constant is ______. ⬜", "options": {"A": "circle", "B": "line", "C": "point", "D": "square"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "Given base BC, ∠B, and inradius r. Construction involves drawing ______. 🔵", "options": {"A": "incircle", "B": "angle bisector of B and C", "C": "line parallel to BC", "D": "perpendicular from B"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Locus of point P such that area(∆PAB)=area(∆PBC) for fixed A,B,C collinear is ______. 📐", "options": {"A": "line parallel to AC", "B": "circle", "C": "line through B", "D": "perpendicular bisector"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "A(1,2), B(4,6). Locus of P such that PA ⟂ PB is ______. 📍", "options": {"A": "line", "B": "circle", "C": "parabola", "D": "ellipse"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "hard", "question": "Given base BC=10 cm, ∠B=45°, and difference of other sides AB-AC=3 cm. Possible triangles? 🔺", "options": {"A": "0", "B": "1", "C": "2", "D": "infinite"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "Locus of point P such that PA/PB = λ (λ≠1) is a circle whose center lies on ______. ⚖️", "options": {"A": "perpendicular bisector", "B": "line AB", "C": "circle with AB diameter", "D": "angle bisector"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "Construct triangle given BC, ∠B, and sum of medians from B and C. Uses ______ loci. 🛠️", "options": {"A": "circle and line", "B": "two circles", "C": "ellipse", "D": "parabola"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "Locus of point P such that ∠APB is always a right angle (A,B fixed) is circle with diameter AB, but excluding ______. 🔵", "options": {"A": "points A and B", "B": "center", "C": "midpoint", "D": "none"}, "correct_answer": "A"}
  ]
}