Difference between revisions of "2004 USAMO Problems/Problem 6"

Revision as of 12:40, 4 July 2013

A circle $\omega$ is inscribed in a quadrilateral $ABCD$ . Let $I$ be the center of $\omega$ . Suppose that

$(AI + DI)^2 + (BI + CI)^2 = (AB + CD)^2$ .

Prove that $ABCD$ is an isosceles trapezoid.

This problem needs a solution. If you have a solution for it, please help us out by adding it.

2004 USAMO (Problems • Resources)
Preceded by Problem 5	Followed by Last problem
1 • 2 • 3 • 4 • 5 • 6
All USAMO Problems and Solutions

Revision as of 13:51, 8 April 2013 (view source) Yrushi (talk \| contribs) m ← Older edit		Revision as of 12:40, 4 July 2013 (view source) Nathan wailes (talk \| contribs) Newer edit →
Line 14:		Line 14:

	{{USAMO newbox\|year=2004\|num-b=5\|after=Last problem}}		{{USAMO newbox\|year=2004\|num-b=5\|after=Last problem}}
		+	{{MAA Notice}}