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Prove that the Points Lie on a Circle

Source: ToT - 2001 Spring Senior O-Level #3

August 17, 2011

geometryperpendicular bisectorgeometry unsolved

Problem Statement

Points

X

and

Y

are chosen on the sides

AB

and

BC

of the triangle

\triangle ABC

. The segments

AY

and

CX

intersect at the point

Z

. Given that

AY = YC

and

AB = ZC

, prove that the points

B

,

X

,

Z

, and

Y

lie on the same circle.

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