Mathematics

Mathematics

Problem

A circle has a chord

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

. a. (i) Prove that

\angle XAY = \angle XBY

. b. (ii) Hence find the value of

y

. c. (iii) Using your value of

y

, calculate

\angle XZY

.

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