Geometry — practice questions, page 3
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In a circle with centre O, the chord AB subtends an angle of 110° at the centre. D is a point on…ABCD is a square of side 8 units, with the vertices named in order around the square. P is the…In triangle ABC, AB = AC and angle A = 36°. The bisector of angle B meets AC at D. What is the…Two circles of radii 9 cm and 4 cm touch each other externally. What is the length of their direct…Which of the following is NOT, in general, a valid criterion for proving that two triangles are…From an external point P, two tangents PA and PB are drawn to a circle with centre O, touching it…In triangle ABC, angle A = 40°. The internal bisector of angle B and the external bisector of the…A line PAQ is tangent to a circle at the point A, and AB is a chord of that circle. The angle…An isosceles triangle has sides 10 cm, 10 cm and 12 cm. What is the radius of its inscribed circle?A right-angled triangle has hypotenuse 61 and one leg of length 11. What is the length of the…In triangle ABC the sides are AB = 7, AC = 9 and BC = 8. D is the midpoint of BC. What is the…In triangle ABC, the point D lies on side BC so that BD : DC = 2 : 5. The area of triangle ABD is…The perimeter of triangle ABC is 42 cm. The midpoints of its three sides are joined to form a…Three parallel lines are cut by two transversals. The first transversal meets them at A, B and C…ABCD is a cyclic quadrilateral with its vertices named in order around the circle. The side AB is…Two circles of radii 13 cm and 15 cm intersect at two points. The distance between their centres…Two circles of radii 8 cm and 3 cm lie outside each other, and the distance between their centres…A quadrilateral ABCD is drawn around a circle so that all four of its sides touch the circle. If…A triangle has sides 5 cm, 12 cm and 13 cm. What is the radius of its inscribed circle?A right-angled triangle has legs 6 cm and 8 cm and hypotenuse 10 cm. A circle drawn outside the…The interior angles of a convex polygon add up to 2340°. How many diagonals does this polygon have?A regular polygon has 9 sides. What angle does one of its sides subtend at the centre of the…Consider a rhombus that is not a square. Which description of its symmetry is correct?The point (5, −3) is first reflected in the line y = x, and the image obtained is then reflected…What is the equation of the straight line passing through the points (2, −1) and (−3, 4)?
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