MathDB

Let

I

be the incenter,

A_1

and

B_1

midpoints of sides

BC

and

AC

of a triangle

\Delta ABC

. Denote by

M

and

N

the midpoints of the arcs

AC

and

BC

of circumcircle of

\Delta ABC

which do contain the other vertex of the triangle. If points

M

I

and

N

are collinear prove that: \begin{align*} \angle AIB_1=\angle BIA_1=90^{\circ} \end{align*}

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