MathDB

Altitudes, Midpoints, and Similar Triangles

Source:

September 8, 2024

geometrysimilar triangles2024

Problem Statement

Let

N_5

be the answer to problem 5.
Triangle

JHU

satisfies

JH=N_5

and

JU=6

. Point

X

lies on

\overline{HU}

such that

\overline{JX}

is an altitude of

\triangle{JHU}

, point

\triangle{HZX}

is the midpoint of

\overline{JU}

, and

\overline{JX}

and

\overline{HY}

intersect at

Z

. Assume that

\triangle{HZX}

is similar to

\triangle{JZY}

(in this vertex order). Compute the area of

\triangle{JHU}

.

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