MathDB

exists circle passing through E,F and tangent to CB,CD, parallelogram

Source: 2018 Argentina OMA L3 p3

June 19, 2020

geometrycircletangentparallelogram

Problem Statement

Let

ABCD

be a parallelogram. An interior circle of the

ABCD

is tangent to the lines

AB

and

AD

and intersects the diagonal

BD

E

and

F

. Prove that exists a circle that passes through

E

and

F

and is tangent to the lines

CB

and

CD