MathDB

The centre

O

of the circumcircle of

\vartriangle ABC

lies inside the triangle. Perpendiculars are drawn rom

O

on the sides. When produced beyond the sides they meet the circumcircle at points

K, M

and

P

. Prove that

\overrightarrow{OK} + \overrightarrow{OM} + \overrightarrow{OP} = \overrightarrow{OI}

, where

I

is the centre of the inscribed circle of

\vartriangle ABC

.
(V Galperin, Moscow)

(051) 3