Difference between revisions of "2024 USAJMO Problems/Problem 1"

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-== Problem ==
+no discussion allowed quite yet!
-Let <math>ABCD</math> be a cyclic quadrilateral with <math>AB=7</math> and <math>CD=8</math>. Points <math>P</math> and <math>Q</math> are selected on line segment <math>AB</math> so that <math>AP=BQ=3</math>. Points <math>R</math> and <math>S</math> are selected on line segment <math>CD</math> so that <math>CR=DS=2</math>. Prove that <math>PQRS</math> is a quadrilateral.
-== Solution 1 (One-liner) ==
-<math>OP=OQ=\sqrt{R^2-3.5^2+0.5^2}=\sqrt{R^2-12}=\sqrt{R^2-4^2+2^2}=OR=OS</math>
 ==See Also==
 {{USAJMO newbox|year=2024|before=First Question|num-a=2}}
 {{MAA Notice}}

2024 USAJMO (Problems • Resources)
Preceded by First Question	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6
All USAJMO Problems and Solutions

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