MathDB

SMT 2021 Geometry #10

Source:

August 9, 2023

geometry

Problem Statement

In acute

\vartriangle ABC

, let points

D

,

E,

and

F

be the feet of the altitudes of the triangle from

A

,

B

,and

C

, respectively. The area of

\vartriangle AEF

is

1

, the area of

\vartriangle CDE

is

2

, and the area of

\vartriangle BF D

is

2 -\sqrt3

. What is the area of

\vartriangle DEF

?

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