MathDB

Find the value of m+n of m/n=&ang;ACB

Source: Bangladesh Mathematical Olympiad 2021 Problem 3

February 20, 2022

geometry

Problem Statement

Let

ABC

be a triangle with incenter

I

. Points

E

and

F

are on segments

AC

and

BC

respectively such that,

AE=AI

and

BF=BI

. If

EF

is the perpendicular bisector of

CI

, then

\angle{ACB}

in degrees can be written as

\frac{m}{n}

where

m

and

n

are co-prime positive integers. Find the value of

m+n