MathDB

Rectangle

ABCD

has an area of 30. Four circles of radius

r_1 = 2

r_2 = 3

r_3 = 5

, and

r_4 = 4

are centered on the four vertices

A

B

C

, and

D

respectively. Two pairs of external tangents are drawn for the circles at A and

C

and for the circles at

B

and

D

. These four tangents intersect to form a quadrilateral

W XY Z

where

\overline{W X}

and

\overline{Y Z}

lie on the tangents through the circles on

A

and

C

. If

\overline{W X} + \overline{Y Z} = 20

, find the area of quadrilateral

W XY Z

. https://cdn.artofproblemsolving.com/attachments/5/a/cb3b3457f588a15ffb4c875b1646ef2aec8d11.png

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