MathDB

Angle geometry

Source: 2024 Nepal TST P5

April 12, 2024

geometryangles

Problem Statement

Let

ABC

be an acute triangle so that

2BC = AB + AC,

with incenter

I{}.

Let

AI{}

meet

BC{}

at point

A'.{}

The perpendicular bisector of

AA'{}

meets

BI{}

and

CI{}

at points

B'{}

and

C'{}

respectively. Let

AB'{}

intersect

(ABC)

at

X{}

and let

XI{}

intersect

AC'{}

at

X'{}.

Prove that

2\angle XX'A'=\angle ABC.{}

(Proposed by Kang Taeyoung, South Korea)

Back to Problems View on AoPS