In a circle with centre

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

O

, chords

AB

and

CD

are equal and intersect at right angles at point

P

inside the circle. (i) Prove that

\angle AOB = \angle COD

. (ii) Prove that

OP

is the bisector of

\angle AOC

. (iii) If

OP = 4\,\text{cm}

and the radius of the circle is

10\,\text{cm}

, calculate the length of each chord.