Difference between revisions of "2022 IMO Problems/Problem 4"
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| − | Problem | + | ==Problem== |
| − | point T inside ABCDE with TB = TD, TC = TE and | + | Let <math>ABCDE</math> be a convex pentagon such that <math>BC = DE</math>. Assume that there is a |
| − | lines CD and CT at points P and Q, respectively. Assume that the points P, B, A, Q occur on their | + | point <math>T</math> inside <math>ABCDE</math> with <math>TB = TD</math>, <math>TC = TE</math> and <math>\angle ABT = \angle TEA</math>. Let line <math>AB</math> intersect |
| − | line in that order. Let line AE intersect lines CD and DT at points R and S, respectively. Assume | + | lines <math>CD</math> and <math>CT</math> at points <math>P</math> and <math>Q</math>, respectively. Assume that the points <math>P, B, A, Q</math> occur on their |
| − | that the points R, E, A, S occur on their line in that order. Prove that the points P, S, Q, R lie on | + | line in that order. Let line <math>AE</math> intersect lines <math>CD</math> and <math>DT</math> at points <math>R</math> and <math>S</math>, respectively. Assume |
| + | that the points <math>R, E, A, S</math> occur on their line in that order. Prove that the points <math>P, S, Q, R</math> lie on | ||
a circle. | a circle. | ||
| + | |||
| + | ==Solution== | ||
| + | https://www.youtube.com/watch?v=-AII0ldyDww [Video contains solutions to all day 1 problems] | ||
Revision as of 05:47, 23 July 2022
Problem
Let 
be a convex pentagon such that 
. Assume that there is a
point 
inside with 
, 
and 
. Let line 
intersect
lines 
and 
at points 
and 
, respectively. Assume that the points 
occur on their
line in that order. Let line 
intersect lines and 
at points 
and 
, respectively. Assume
that the points 
occur on their line in that order. Prove that the points 
lie on
a circle.
Solution
https://www.youtube.com/watch?v=-AII0ldyDww [Video contains solutions to all day 1 problems]
