MathDB

Easy Geometry

Source: 2021 MEMO I-3

September 5, 2021

geometrycircumcircleConcyclicptolemy sinus lemmaComputer problems

Problem Statement

Let

ABC

be an acute triangle and

D

an interior point of segment

BC

. Points

E

and

DF

lie in the half-plane determined by the line

BC

containing

A

such that

DE

is perpendicular to

BE

and

DE

is tangent to the circumcircle of

ACD

, while

DF

is perpendicular to

CF

and

DF

is tangent to the circumcircle of

ABD

. Prove that the points

A, D, E

and

F

are concyclic.

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