MathDB

Let

ABC

be a triangle such that

AB = 26, AC = 30,

and

BC = 28

. Let

C'

and

B'

be the reflections of the circumcenter

O

over

AB

and

AC

, respectively. The length of the portion of line segment

B'C'

inside triangle

ABC

can be written as

\frac{p}{q}

, where

p,q

are relatively prime positive integers. Compute

p+q

17