2022 IMO Problems/Problem 4

Problem

Let $ABCDE$ be a convex pentagon such that $BC = DE$ . Assume that there is a point $T$ inside $ABCDE$ with $TB = TD$ , $TC = TE$ and $\angle ABT = \angle TEA$ . Let line $AB$ intersect lines $CD$ and $CT$ at points $P$ and $Q$ , respectively. Assume that the points $P, B, A, Q$ occur on their line in that order. Let line $AE$ intersect lines $CD$ and $DT$ at points $R$ and $S$ , respectively. Assume that the points $R, E, A, S$ occur on their line in that order. Prove that the points $P, S, Q, R$ lie on a circle.

Solution

https://www.youtube.com/watch?v=-AII0ldyDww [Video contains solutions to all day 2 problems]

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2022 IMO Problems/Problem 4

Problem

Solution