AK is drawn in an isosceles triangle ABC where AB = BC. Find the perimeter of triangle ABC if AC = 10cm KC = 6cm.

Let the length of the segment ВK = X cm.

Since the triangle ABC is isosceles, then the side AB = BC, then AB = (X + 6) cm.

By condition, AK is the bisector of the angle BAC, then by the property of the bisector of the triangle, the segments kA which the bisector divides the opposite side into segments that are proportional to the adjacent sides.

KС / KВ = AC / AB.

6 / X = 10 / (X + 6).

10 * X = 6 * X + 36.

4 * X = 36.

X = BK = 36/4 = 9 cm.

Then BC = AB = СK + ВK = 6 + 9 = 15 cm.

Let’s define the perimeter of the triangle ABC.

P = 2 * BC + AC = 2 * 15 + 10 = 30 + 10 = 40 cm.