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Equal segments imply angle bisector

Source: 2007 Bulgarian Autumn Math Competition, Problem 11.3

March 17, 2022
geometryangle bisectorequal segmentsequal angles

Problem Statement

In △ABC\triangle ABC we have that CC1CC_{1} is an angle bisector. The points P∈C1BP\in C_{1}B, Q∈BCQ\in BC, R∈ACR\in AC, S∈AC1S\in AC_{1} satisfy C1P=PQ=QCC_{1}P=PQ=QC and CR=RS=SC1CR=RS=SC_{1}. Prove that CC1CC_{1} bisects ∠SCP\angle SCP.
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