Problem:
In △ABC with a right angle at C, point D lies in the interior of AB and point E lies in the interior of BC so that AC=CD,DE=EB, and the ratio AC:DE=4:3. What is the ratio AD:DB?
Answer Choices:
A. 2:3
B. 2:5
C. 1:1
D. 3:5
E. 3:2
Solution:
Let AC=DC=4x and DE=BE=3x. Because ∠A≅∠ADC,∠B≅∠EDB, and ∠A and ∠B are complementary, it follows that ∠CDE is a right angle. Thus CE=5x. Let F and G lie on AB so that CF and EG are perpendicular to AB. Then it follows that
