In parallelogram ABCD, the bisector of angle C intersects side AD at point N, AN = 6, ND = 10. Find the perimeter.

P ABCD = AB + BC + CD + AD

BC = AD = 6 + 10 = 16 (opposite sides of the parallelogram are equal)

Find the lengths of the sides AB and CD:

Angle ВСN = angle DCN (since CN is the bisector of angle С); angle BCN = angle CND (these are internal criss-crossing angles with parallel lines BC and AD and secant CN). This means that the angles DCN and CND will be equal and therefore the triangle NDC will be isosceles. In an isosceles triangle, the sides are equal, so ND = CD = 10.

AB = CD = 10.

P ABCD = 10 + 16 + 10 + 16 = 52.

Answer. 52.