MathDB

(CADB)=, 2 intersecting circles, AC_|_AB, BD_|_AB 2019 BMT Individual 13

Source:

January 5, 2022

geometrycircles

Problem Statement

Two circles

O_1

and

O_2

intersect at points

A

and

B

. Lines

\overline{AC}

and

\overline{BD}

are drawn such that

C

is on

O_1

and

D

is on

O_2

and

\overline{AC} \perp \overline{AB}

and

AB= 60

. If minor arc

AB= 45

degrees relative to

O_1

and minor arc

AB= 60

degrees relative to

O_2

and the radius of

O_2 = 10

, the area of quadrilateral

CADB

can be expressed in simplest form as

a + b\sqrt{k} + c\sqrt{\ell}

. Compute

a + b + c + k +\ell

.

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