MathDB

1

Part of 2012 Greece Junior Math Olympiad

Problems(1)

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

Source:

7/14/2019
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.
geometryangle bisectorcircumcircle