2023 CMO Problems/Problem 5

In an acute triangle $\triangle A B C, K$ is a point on the extension of $B C$ . Through $K$ , draw lines parallel to $A B$ and $A C$ , denoted as $K P$ and $K Q$ respectively, such that $B K=B P$ and $C K=C Q$ . Let the circumcircle of $\triangle K P Q$ intersect $A K$ at point $T$ . Prove: (1) $\angle B T C+\angle A P B=\angle C Q A$ ; (2) $A P \cdot B T \cdot C Q=A Q \cdot C T \cdot B P$ .

Solution 1

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2023 CMO(CHINA) (Problems • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6
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2023 CMO Problems/Problem 5

Solution 1

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