In a circle with centre

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

Problem

O

, four points

A

B

C

and

D

are taken in order on the circumference such that

\angle AOB=80^{\circ}

\angle BOC=100^{\circ}

\angle COD=80^{\circ}

and

\angle DOA=100^{\circ}

. (i) Prove that chords

AB

and

CD

are equal in length. (ii) Prove that chords

BC

and

DA

are equal in length. (iii) Compare the lengths of chords

AB

and

BC

, giving complete justification for your conclusion.