MathDB

2021.7

Part of Ukraine Correspondence MO - geometry

Problems(1)

DE passes through I, if <BAC = 60 ^o and BD = CE = BC

Source: 2021 All-Ukrainain Correspondence MO , grades 5-12 p7

6/24/2022
Let II be the center of a circle inscribed in triangle ABCABC, in which ∠BAC=60o\angle BAC = 60 ^o and AB≠ACAB \ne AC. The points DD and EE were marked on the rays BABA and CACA so that BD=CE=BCBD = CE = BC. Prove that the line DEDE passes through the point II.
geometrycollinearincenterequal segmentsUkraine Correspondence