MathDB

2 lines intersect on a circle tangent to 2 sides of a triangle

Source: (2022 -) 2023 XVI Dürer Math Competition Finals Day 1 E1

May 25, 2024

geometryconcurrentConcyclic

Problem Statement

ABC

is an isosceles triangle. The base

BC

1

cm long, and legs

AB

and

AC

are

2

cm long. Let the midpoint of

AB

F

, and the midpoint of

AC

G

. Additionally,

k

is a circle, that is tangent to

AB

and A

C

, and it’s points of tangency are

F

and

G

accordingly. Prove, that the intersection of

CF

and

BG

falls on the circle

k