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MathNet 2002 — Part 01 Question 112

Math Olympiad Vault · MathNet 2002 — Part 01

Question 112

Two circles intersect at points $A$ and $B$. Through the point $B$ a straight line is drawn, intersecting the first circle at $K$ and the second circle at $M$. A line parallel to $AM$ is tangent to the first circle at $Q$. The line $AQ$ intersects the second circle again at $R$.


a. Prove that the tangent to the second circle at $R$ is parallel to $AK$.


b. Prove that these two tangents are concurrent with $KM$.