MathDB
Weird angle condition geo

Source: India EGMO 2021 TST P3

November 18, 2021
geometrycircumcircleincenterangle bisector

Problem Statement

In acute △ABC\triangle ABC with circumcircle Γ\Gamma and incentre II, the incircle touches side ABAB at FF. The external angle bisector of ∠ACB\angle ACB meets ray ABAB at LL. Point KK lies on the arc CBCB of Γ\Gamma not containing AA, such that ∠CKI=∠IKL\angle CKI=\angle IKL. Ray KIKI meets Γ\Gamma again at D≠KD\ne K. Prove that ∠ACF=∠DCB\angle ACF =\angle DCB.
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