MathDB

Let

D

be a point different from the vertices on the side

BC

of a triangle

ABC.

Let

I, \: I_1

and

I_2

be the incenters of the triangles

ABC, \: ABD

and

ADC,

respectively. Let

E

be the second intersection point of the circumcircles of the triangles

AI_1I

and

ADI_2,

and

F

be the second intersection point of the circumcircles of the triangles

AII_2

and

AI_1D.

Prove that if

AI_1=AI_2,

then

\frac{EI}{FI} \cdot \frac{ED}{FD}=\frac{{EI_1}^2}{{FI_1}^2}.

Problem Statement