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<KDA = <BCA or <KDA = <KBA. if KD = DC, <BAC = 1/2 <KDC,<DAC = 1/2<KB

Source: - All-Russian MO 2003 Regional (R4) 11.2

September 17, 2024
geometryanglesequal angles

Problem Statement

On the diagonal ACAC of a convex quadrilateral ABCDABCD is chosen such a point KK such that KD=DCKD = DC, ∠BAC=12∠KDC\angle BAC = \frac12 \angle KDC, ∠DAC=12∠KBC\angle DAC = \frac12 \angle KBC. Prove that ∠KDA=∠BCA\angle KDA = \angle BCA or ∠KDA=∠KBA\angle KDA = \angle KBA.
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