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prove that AC bisects <DAE, circles related (Greece Junior 2012)

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July 14, 2019
geometryangle bisectorcircumcircle

Problem Statement

Let ABCABC be an acute angled triangle (with AB<AC<BCAB<AC<BC) inscribed in circle c(O,R)c(O,R) (with center OO and radius RR). Circle c1(A,AB)c_1(A,AB) (with center AA and radius ABAB) intersects side BCBC at point DD and the circumcircle c(O,R)c(O,R) at point EE. Prove that side ACAC bisects angle ∠DAE\angle DAE.
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