Mock AIME 2 2006-2007 Problems/Problem 12
Contents
Problem
In quadrilateral and is defined to be the intersection of the diagonals of . If , and the area of is where are relatively prime positive integers, find
Note*: and refer to the areas of triangles and
Solution
is a cylic quadrilateral.
Let
~
Also, from the Power of a Point Theorem,
Notice
It is given
Note that
Then and
Thus we need to find
Note that is isosceles with sides so we can draw the altitude from D to split it to two right triangles.
Thus
See Also
Mock AIME 2 2006-2007 (Problems, Source) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |
Problem Source
AoPS users 4everwise and Altheman collaborated to create this problem.