In the triangle MNK, the bisectors intersect at point O. The distance from point O

In the triangle MNK, the bisectors intersect at point O. The distance from point O to the side MN = 6 cm, NK = 10 cm. Find the area of the triangle NOK.

We know that the intersection point of the bisectors is the center of the circle inscribed in the triangle, then the distance from O to the side is MN = r.
Thus, the distance from O to the side can be expressed as: NK = MN = 6.
S∆NOK = 1/2 * 6 * 10;
S∆NOK = 30 cm².
Answer: S∆NOK = 30 cm².