MathDB

Isosceles trapezoid

ABCD

has side lengths

AB = 6

and

CD = 12

, while

AD = BC

. It is given that

O

, the circumcenter of

ABCD

, lies in the interior of the trapezoid. The extensions of lines

AD

and

BC

intersect at

T

. Given that

OT = 18

, the area of

ABCD

can be expressed as

a + b\sqrt{c}

where

a

b

, and

c

are positive integers where

c

is not divisible by the square of any prime. Compute

a+b+c

.
Proposed by Andrew Wen

17