KöMaL 2006 K75

The point $K$ lies on each of the circles of radius $r$ centred at the points $K_1$, $K_2$, $K_3$. The other common points of two of the three circles are $P$, $Q$, and $R$. Show that the triangles $K_1 K_2 K_3$ and PQR are congruent.