MathDB

SMT 2019 Geometry #8

Source:

August 8, 2023

geometry

Problem Statement

In the coordinate plane, a point

A

is chosen on the line

\ell_1

in the first quadrant. Two perpendicular lines

\ell_1

and

\ell_2

intersect at A where

\ell_1

has slope

m > 1

. Let

\ell_1

intersect the

x

-axis at

B

, and

\ell_2

intersects the

x

and

y

axes at

C

and

D

, respectively. Suppose that line

BD

has slope

-m

and

BD = 2

. Compute the length of

CD

.

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