MathDB

Concyclic Points and Angle Bisectors

Source:

September 7, 2024

geometryangle bisectorcircumcircle2024

Problem Statement

Points

A

,

B

,

C

, and

D

lie on a circle

\Gamma

, in that order, with

AB=5

and

AD=3

. The angle bisector of

\angle ABC

intersects

\Gamma

at point

E

on the opposite side of

\overleftrightarrow{CD}

as

A

and

B

. Assume that

\overline{BE}

is a diameter of

\Gamma

and

AC=AE

. Compute

DE

.

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