Problem:
Point is inside equilateral . Points , and are the feet of the perpendiculars from to , and , respectively. Given that , , and , what is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the side length of be . Then the areas of , , and are, respectively, , and . The area of is the sum of these, which is . The area of may also be expressed as , so . The unique positive solution for is .
The problems on this page are the property of the MAA's American Mathematics Competitions