# Geometry Problem 1322: Triangle, Angle Bisector, Circumcircle, Chord,
Secant, Sum of two Angles

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In a triangle ABC, X is a point on BC and AY is the bisector of the angle
CAX as shown in the figure. The circumcircle of the triangle ABX cuts AY
at Z. BZ extended meets AC at W. Prove that angle XBZ + angle WXZ = angle
XWY. *This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.*

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Geometry Problems

1311-1320

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Triangle

Angle Bisector

Circle

Circumcircle

Secant

Angles

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Sketch of problem 1322

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