Difference between revisions of "Mock AIME I 2012 Problems/Problem 3"
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Latest revision as of 17:31, 7 April 2012
Problem
Triangle has , , . The trisection points of are and , with . Segments and are extended to points and such that and . The area of pentagon is , where and are relatively prime positive integers. Find .
Solution
Use Heron's formula to find . Also note from the trisection that . Now . Similarly, . From this we deduce that
(i)
(ii) Similarly to (i),
(iii) with ratio , so
The area of our pentagon is . The answer is .