In the triangle MNK, the bisectors intersect at point O. Distance from point O to the side MN = 6cm

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

Since point O is the intersection point of the bisectors of the triangle, it is the center of the triangle, and therefore the center of the circle inscribed in the triangle.

The segments OA and OB are perpendiculars to the sides of the triangle, which means there are the radii of the inscribed circle.

Then ОА = ОВ = 6 cm.

The area of the LCM triangle will be equal to:

Snok = НK * ОВ / 2 = 10 * 6/2 = 30 cm2.

Answer: The area of the НОК triangle is 30 cm2.