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if <BLA= <BAC$, then BP = CP (Caucasus 2015 geometry for 9th grade)

Source: I Caucasus 2015 9.3

September 6, 2018
geometryequal anglesequal segmentscircumcircleangle bisector

Problem Statement

Let ALAL be the angle bisector of the acute-angled triangle ABCABC. and ω\omega be the circle circumscribed about it. Denote by PP the intersection point of the extension of the altitude BHBH of the triangle ABCABC with the circle ω\omega . Prove that if ∠BLA=∠BAC\angle BLA= \angle BAC, then BP=CPBP = CP.
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