MathDB

segment of projections is half as sidelength, right triangle inscribed in right

Source: 2020 Austrian Federal Competition For Advanced Students, Part 1, p2

November 22, 2020

geometryequal segmentsright triangle

Problem Statement

Let

ABC

be a right triangle with a right angle in

C

and a circumcenter

U

. On the sides

AC

and

BC

, the points

D

and

E

lie in such a way that

\angle EUD = 90 ^o

. Let

F

and

G

be the projection of

D

and

E

AB

, respectively. Prove that

FG

is half as long as

AB

.
(Walther Janous)