A circle has a chord

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

Problem

XY

. Two points

A

and

B

lie on the circumference on the same side of

XY

such that

\angle XAY = (5y - 7)^\circ

and

\angle XBY = (3y + 29)^\circ

. The diameter through

Y

meets the circle again at

Z

. (i) Prove that

\angle XAY = \angle XBY

. (ii) Hence find the value of

y

. (iii) Using your value of

y

, calculate

\angle XZY