Geometry — practice questions, page 3
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In triangle ABC, DE ∥ BC with D on AB and E on AC. The area of triangle ADE is 25 cm² and the area…The area of triangle ABC is 60 cm². D lies on BC with BD : DC = 2 : 3, and E is the midpoint of…Two vertical poles of heights 6 m and 11 m stand on level ground 12 m apart. What is the distance…Which of the following is NOT a valid test for the congruence of two triangles?A right-angled triangle has a perimeter of 30 cm and an area of 30 cm². What is the length of its…M is the midpoint of the hypotenuse AC of triangle ABC, which is right-angled at B with AB = 5 cm…In triangle ABC, DE ∥ BC with D on AB and E on AC. If AD = x cm, DB = (x − 2) cm, AE = (x + 2) cm…AD is the altitude from A to BC in triangle ABC, where AB = 13 cm, AC = 20 cm and BC = 21 cm. Find…The three medians of a triangle measure 9 cm, 12 cm and 15 cm. What is the area of the triangle?A chord of a circle of radius 17 cm is at a distance of 8 cm from the centre. What is the length…An arc of a circle subtends an angle of 110° at the centre. What angle does it subtend at a point…A, B, C and D lie on a circle and the diagonals AC and BD of quadrilateral ABCD meet at E. If ∠ADB…AB and CD are equal chords of a circle with centre O. If ∠AOB = 72°, find ∠OCD.A chord subtends a right angle at the centre of a circle of radius 5√2 cm. How long is the chord?Two parallel chords of lengths 48 cm and 14 cm lie on the same side of the centre of a circle of…A and B are points on a circle with centre O, and ∠OAB = 28°. C is a point on the minor arc AB.…PQRS is a cyclic quadrilateral with ∠P = (x + 20)°, ∠Q = (2x − 10)° and ∠R = (3x − 20)°. Find ∠S.Two chords AB and CD of a circle cut each other at an interior point P. If AP = 6 cm, PB = 4 cm…From a point P outside a circle, a secant cuts the circle at A and B (PA = 4 cm, AB = 5 cm), and…A chord AB of a circle is equal in length to the radius. What angle does AB subtend at a point on…Chords AB and CD of a circle intersect at E inside the circle. The arc AC that faces ∠AEC measures…Two secants PAB and PCD meet at a point P outside a circle. The far arc BD measures 130° and the…ABCD is a cyclic quadrilateral with AB ∥ DC and ∠DAB = 70°. Find ∠ABC.AB is a diameter of a circle with centre O, and C is a point on the circle with ∠BOC = 64°. D is a…Through how many circles can three non-collinear points all pass?
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