MathDB
Problem 21, Spring 2005 , HS

Source:

June 23, 2011
rationumber theoryrelatively prime

Problem Statement

In the diagram below ∠CAB,∠CBD \angle CAB, \angle CBD, and ∠CDE\angle CDE are all right angles with side lengths AC=3AC = 3, BC=5BC = 5, BD=12BD = 12, and DE=84DE = 84. The distance from point EE to the line ABAB can be expressed as the ratio of two relatively prime positive integers, mm and nn. Find m+nm + n.
[asy] size(300); defaultpen(linewidth(0.8)); draw(origin--(3,0)--(0,4)--cycle^^(0,4)--(6,8)--(3,0)--(30,-4)--(6,8)); label("AA",origin,SW); label("BB",(0,4),dir(160)); label("CC",(3,0),S); label("DD",(6,8),dir(80)); label("EE",(30,-4),E);[/asy]
Back to ProblemsView on AoPS