2022 IMO Problems/Problem 4: Difference between revisions
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Problem 4. Let ABCDE be a convex pentagon such that BC = DE. Assume that there is a | Problem 4. Let ABCDE be a convex pentagon such that BC = DE. Assume that there is a | ||
point T inside ABCDE with T B = TD, T C = T E and ∠ABT = | point T inside ABCDE with T B = TD, T C = T E and ∠ABT = ∠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 | 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 | 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 | 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. | a circle. | ||
Revision as of 23:43, 16 July 2022
Problem 4. Let ABCDE be a convex pentagon such that BC = DE. Assume that there is a point T inside ABCDE with T B = TD, T C = T E and ∠ABT = ∠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.
