MathDB

Let

\triangle ABC

be an acute-angled triangle with its incenter

I

. Suppose that

N

is the midpoint of the arc \overarc{BAC} of the circumcircle of triangle

\triangle ABC

, and

P

is a point such that

ABPC

is a parallelogram.Let

Q

be the reflection of

A

over

N

and

R

the projection of

A

\overline{QI}

. Show that the line

\overline{AI}

is tangent to the circumcircle of triangle

\triangle PQR

Proposed by Patrik Bak - Slovakia

Problem Statement