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CK_|_AB if AK=KB+PC, BC=AP, <APC +<ABC=180^o (2020 Novosibirsk Oral Geo Oly 7.5)

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April 27, 2021
geometryperpendicularequal segments

Problem Statement

Point PP is chosen inside triangle ABCABC so that ∠APC+∠ABC=180o\angle APC+\angle ABC=180^o and BC=AP.BC=AP. On the side ABAB, a point KK is chosen such that AK=KB+PCAK = KB + PC. Prove that CK⊥ABCK \perp AB.
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