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MathNet 2022-part-05 — 197 problems (EN–VI) Question 171

Math Olympiad Vault · MathNet 2022-part-05 — 197 problems (EN–VI)

Question 171

Consider the circumscribed circle of an obtuse triangle $ABC$ with an obtuse angle $B$. Tangents to this circle at points $A$ and $B$ meet at point $P$, and the perpendicular to the line $BC$ at point $B$ intersects $AC$ at point $K$. Prove, that $PA = PK$.

(Danylo Khilko)