Mock AIME 5 2005-2006 Problems/Problem 12
Contents
Problem
Let be a triangle with , , and . Let be the foot of the altitude from to and be the point on between and such that . Extend to meet the circumcircle of at . If the area of triangle is , where and are relatively prime positive integers, find .
Solution
Let area of be denoted by .
By Heron's theorem , We get
By pythagoras theorem on , We get
So, .
Again applying pythagoras theorem on , We get,
As and share same height ,
So,
Thus
So,
Now, [Vertical angle]
[shares same chord BF]
So, is simillar to
Now,
So,
Now,
Thus required answer=
~by NOOBMASTER_M
Solution
See also
Mock AIME 5 2005-2006 (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 |