MathDB

2014.10

Part of Ukraine Correspondence MO - geometry

Problems(1)

one of lines DE,DF passes through incenter of ABC, circumcircle related

Source: 2014 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p10

4/27/2021
In the triangle ABCABC, it is known that AC<ABAC <AB. Let ℓ\ell be tangent to the circumcircle of triangle ABCABC drawn at point AA. A circle with center AA and radius ACAC intersects segment ABAB at point DD, and line ℓ\ell at points EE and FF. Prove that one of the lines DEDE and DFDF passes through the center inscribed circle of triangle ABCABC.
geometryincentercircumcircleUkraine Correspondence