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Simson lines on the AIME

Source: 2021 AIME I P9

March 11, 2021

AMCAIME2021 AIME I

Problem Statement

Let

ABCD

be an isosceles trapezoid with

AD=BC

and

AB<CD.

Suppose that the distances from

A

to the lines

BC,CD,

and

BD

are

15,18,

and

10,

respectively. Let

K

be the area of

ABCD.

Find

\sqrt2 \cdot K.

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