MathDB

2020.10.5.1

Part of Kyiv City MO Seniors 2003+ geometry

Problems(1)

<EFD=<ACD+<ECB wanted, points on semicircle (2020 Kyiv City MO 10.5.1 11.4.1)

Source:

9/20/2020
Let Γ\Gamma be a semicircle with diameter ABAB. On this diameter is selected a point CC, and on the semicircle are selected points DD and EE so that EE lies between BB and DD. It turned out that ∠ACD=∠ECB\angle ACD = \angle ECB. The intersection point of the tangents to Γ\Gamma at points DD and EE is denoted by FF. Prove that ∠EFD=∠ACD+∠ECB\angle EFD=\angle ACD+ \angle ECB.
geometrysemicircleanglesequal angles