MathDB

computational geo right triangle, AF _|_ EI, AI/IF=4/3

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist G2 day1

September 23, 2021

geometryright triangle

Problem Statement

Consider

\vartriangle ABC

right at

B, F

a point such that

B - F - C

and

AF

bisects

\angle BAC

,

I

a point such that

A - I - F

and CI bisect

\angle ACB

, and

E

a point such that

A- E - C

and

AF \perp EI

. If

AB = 4

and

\frac{AI}{IF}={4}{3}

, determine

AE

.
Notation:

A-B-C

means than points

A,B,C

are collinear in that order i.e.

B

lies between

A

and

C

.

Back to Problems View on AoPS