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Equal Lines in Two Circles

Source: Irish Mathematical Olympiad - Paper 2 - 2008 -Question 2

May 11, 2008

geometrytrapezoidgeometry proposed

Problem Statement

Circles

S

and

T

intersect at

P

and

Q

, with

S

passing through the centre of

T

. Distinct points

A

and

B

lie on

S

, inside

T

, and are equidistant from the centre of

T

. The line

PA

meets

T

again at

D

. Prove that |AD| \equal{} |PB|.