Find the perimeter of an isosceles triangle, the lateral side of which is divided by the point

Find the perimeter of an isosceles triangle, the lateral side of which is divided by the point of contact with the inscribed circle into 6 m and 8 m segments, if we count the bases.

Let’s denote this triangle by ABC, where C is the apex of the triangle.

Let K denote the point that divides the side of BC into two segments BK = 6, KC = 8.

We denote the midpoint of AB as point M.

Find side BC.

BC = BK + KC = 6 + 8 = 14.

Since the triangle is isosceles, then AC = BC = 14.

Tangents drawn from one point have the same length, that is, BM = BK = 6.

But AB = 2 * BM = 12.

That is, the perimeter of triangle ABC is 14 + 14 + 12 = 40.

Answer: The perimeter of triangle ABC is 40 m.