In a circle with centre

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

O

, two chords

PQ

and

RS

are equal in length. (i) Let

OP

and

OR

be perpendicular to

PQ

and

RS

X

and

Y

respectively. Prove that

OX = OY

. (ii) If

PQ = RS = 24\,\text{cm}

and the radius of the circle is

13\,\text{cm}

, find the common distance of each chord from the centre.