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Exam-Style Questions on Intersecting ChordsProblems on Intersecting Chords adapted from questions set in previous Mathematics exams. |
1. | GCSE Higher |
A, B, D and D are points on a circle, centre O.
BD is a diameter of the circle.
BD and AC intersect at the point T.
OD= 15 cm, BT = 9 cm and CT = 18 cm.
Work out the length of AT.
2. | GCSE Higher |
The length of a tangent from a point \(S\) to a point on the circumference of a circle, with centre at \(O\), is 1800 km. The length of a radius of this circle is 750 km.
(a) Show how the intersecting secant theorem can be used to find the distance from \(S\) to \(O\).
(b) Check you solution to part (a) by using Pythagoras' theorem. All working must be clearly shown.
3. | GCSE Higher |
T, Q, R and S are four points on a circle in this diagram not drawn to scale.
PTQ and PSR are straight lines.
PT = 10 cm, TQ = 14 cm and SR = 8 cm.
Angle TPS = 32°
(a) Calculate the length of PS.
(b) Calculate the length of SQ
Give your answer correct to 3 significant figures.
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