MathDB

All possible lengths of sides in that triangle

Source: OMEC Ecuador National Olympiad Final Round 2023 N3 P6 day 2

November 6, 2024

geometrynational olympiad

Problem Statement

Let

DE

the diameter of a circunference

\Gamma

. Let

B, C

\Gamma

such that

BC

is perpendicular to

DE

, and let

Q

the intersection of

BC

with

DE

. Let

P

a point on segment

BC

such that

BP=4PQ

. Let

A

the second intersection of

PE

with

\Gamma

. If

DE=2

and

EQ=\frac{1}{2}

, find all possible values of the sides of triangle

ABC