2003 AIME II Problems/Problem 7
Problem
Find the area of rhombus given that the radii of the circles circumscribed around triangles and are and , respectively.
Solution
The diagonals of the rhombus perpendicularly bisect each other. Call half of diagonal BD and half of diagonal AC . The length of the four sides of the rhombus is . The area of any triangle can be expressed as , where a, b, and c are the sides and is the circumradius. Thus, the area of is . Also, the area of is . Setting these two expressions equal to each other and simplifying gives b=2a. Substitution yields and , so the area of the rhombus is .
See also
2003 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |