MathDB

Let

ABCD

be a convex quadrilateral.

O

is the intersection of

AC

and

BD

AO=3

BO=4

CO=5

DO=6

X

and

Y

are points in segment

AB

and

CD

respectively, such that

X,O,Y

are collinear. The minimum of

\frac{XB}{XA}+\frac{YC}{YD}

can be written as

\frac{a\sqrt{c}}{b}

, where

\frac{a}{b}

is in lowest term and

c

is not divisible by any square number greater then

1

. What is the value of

10a+b+c

Problem Statement