Problem:
The isosceles right triangle ABC has right angle at C and area 12.5. The rays trisecting ∠ACB intersect AB at D and E. What is the area of △CDE?
Answer Choices:
A. 352
B. 4503−75
C. 8153
D. 250−253
E. 625
Solution:
Because the area is 12.5, it follows that AC=BC=5. Label D and E so that D is closer to A than to B. Let F be the foot of the perpendicular to AC passing through D. Let h=FD. Then AF=h because △ADF is an isosceles right triangle, and CF=h3 because △CDF is a 30−60−90∘ triangle. So h+h3=AC=5 and
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