Cambridge IGCSE Mathematics practice

exam practice - Understand and apply the symmetry properties of circles, including that equal chords are at the same distance from the center, the perpendicular bisector of a chord goes through the center, and that tangents drawn from a point outside the circle are of equal length. Use these properties to justify answers in geometrical problems. - Circle theorems II

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At a glance

Paper

Marks

Topic

Circle theorems II

Exam-style question

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Paper 2Core or Extended Mathematics3 marks

Tangents from an External Point

Diagram Description

Point P lies outside the circle. Two tangents, PA and PB, are drawn from P to the circle, touching it at points A and B respectively.

Point	Description
P	External point
A	Point of tangency on the circle
B	Point of tangency on the circle

a
Show That the lengths of tangents PA and PB are equal.
Your answer
Aim for approximately 3 distinct marking points.
[3]

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Maths method check

Topic focus: Circle theorems II.
Question style: structured_mathematics.
Reasoning demand: reasoning.
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Paper 2Core or Extended Mathematics2 marks

Diagram Description

In the circle below, chords AB and CD are equal in length. The perpendicular bisector of chord AB passes through the center O of the circle.

a
Explain Why are chords AB and CD the same distance from the center O?
Your answer
Aim for approximately 2 distinct marking points.
[2]