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RMO 2015 Karnataka geometry II, intersecting circles

Source: CRMO 2015 region 4 (Karnataka) p5

September 30, 2018

geometrycirclesequal segments

Problem Statement

Two circles

\Gamma

and

\Sigma

intersect at two distinct points

A

and

B

. A line through

B

intersects

\Gamma

and

\Sigma

again at

C

and

D

, respectively. Suppose that

CA=CD

. Show that the centre of

\Sigma

lies on

\Gamma