MathDB

AI tangent to (BMI) if AI _|_ IN

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2022 p6

March 26, 2024

tangentgeometry

Problem Statement

Consider

ABC

with

AC > AB

and incenter

I

. The midpoints of

\overline{BC}

and

\overline{AC}

are

M

and

N

, respectively. If

\overline{AI}

is perpendicular to

\overline{IN}

, then prove that

\overline{AI}

is tangent to the circumscribed circle of

\vartriangle BMI