Mathematics

Problem

In a circle with centre

O

, two chords

PQ

and

RS

are equal in length. a. (i) Let

OP

and

OR

be perpendicular to

PQ

and

RS

X

and

Y

respectively. Prove that

OX = OY

. b. (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.