Geometry — practice questions, page 4
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C is a point on a circle with centre O, and ∠ACB = 48°, where A and B also lie on the circle and C…In a circle of radius 5 cm, AB and AC are two chords, each 6 cm long. Find the length of BC.Two concentric circles have radii 10 cm and 6 cm. Find the length of the chord of the larger…ABCD is a cyclic quadrilateral whose diagonals meet at E. If AB = BC, ∠BAC = 30° and ∠DBC = 70°,…The longest chord of a circle is 26 cm. How far from the centre is a chord of length 10 cm?A, B, C and D lie on a circle in that order. ∠ABD is twice ∠DBC and ∠ADC = 105°. Find ∠DAC.In a circle of radius 6 cm, a chord subtends an angle of 120° at the centre. Find the length of…Two parallel chords of a circle, of lengths 10 cm and 24 cm, lie on opposite sides of the centre…A point P lies 12 cm from the centre of a circle of radius 13 cm. What is the length of the…A point is 25 cm from the centre of a circle of radius 7 cm. How long is the tangent drawn from…PA and PB are tangents to a circle from an external point P, and ∠APB = 70°. Find ∠PAB.PA and PB are tangents from P to a circle with centre O, and ∠OPA = 32°. Find ∠AOB.AT is a tangent to a circle at A, and the chord AB makes an angle of 58° with AT. C is a point on…Triangle ABC is inscribed in a circle, and CT is the tangent at C drawn on the side of B. If ∠BCT…The incircle of triangle ABC touches BC, CA and AB at D, E and F. If AF = 4 cm, BD = 6 cm and CE =…Triangle ABC has AB = 8 cm, BC = 10 cm and CA = 12 cm. Its incircle touches AB at F. Find AF.A right-angled triangle has legs 8 cm and 15 cm. What is the radius of its incircle?A parallelogram is drawn so that a circle touches all four of its sides. One side of the…The centres of two circles of radii 7 cm and 5 cm are 20 cm apart. How long is a transverse…Two circles of radii 9 cm and 4 cm touch each other externally. Find the length of their direct…Circles of radii 5 cm and 3 cm have centres exactly 8 cm apart. How many common tangents can be…How many common tangents do two circles of radii 6 cm and 4 cm have if their centres are 3 cm apart?From a point P, 12 cm from the centre of a circle of radius 6 cm, two tangents are drawn. What is…Tangents PA and PB are drawn to a circle of radius 5 cm from a point P that is 13 cm from the…Three circles touch one another externally. The distances between their centres are 7 cm, 8 cm and…
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