Difference between revisions of "2000 AIME II Problems/Problem 10"
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{{AIME box|year=2000|n=II|num-b=9|num-a=11}} | {{AIME box|year=2000|n=II|num-b=9|num-a=11}} |
Revision as of 20:35, 18 March 2008
Problem
A circle is inscribed in quadrilateral , tangent to
at
and to
at
. Given that
,
,
, and
, find the square of the radius of the circle.
Solution
Call the center of the circle . By drawing the lines from
tangent to the sides and from
to the vertices of the quadrilateral, eight congruent right triangles are formed.
Thus, , or
.
Take the of both sides and use the identity for
to get
.
Use the identity for again to get
.
Solving gives .
2000 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |