IGO 2016 Medium/4

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IGO 2016 Medium/4

Post Number:#1  Unread postby Thamim Zahin » Tue Jan 10, 2017 4:03 pm

4. Let $w$ be the circumcircle of right-angled triangle $ABC (\angle A = 90)$. Tangent to $w$ at point $A$ intersects the line $BC$ in point $P$. Suppose that $M$ is the midpoint of (the smaller) arc $AB$, and $PM$ intersects $w$ for the second time in $Q$. Tangent to $w$ at point $Q$ intersects $AC$ in $K$. Prove that $\angle PKC = 90$.
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Thamim Zahin
 
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