MathDB

2012-2013 Winter OMO #19

Source:

January 16, 2013

Online Math Opengeometryrectanglenumber theoryrelatively prime

Problem Statement

A,B,C

are points in the plane such that

\angle ABC=90^\circ

. Circles with diameters

BA

and

BC

meet at

D

. If

BA=20

and

BC=21

, then the length of segment

BD

can be expressed in the form

\frac{m}{n}

where

m

and

n

are relatively prime positive integers. What is

m+n

?
Ray Li