A circle is inscribed in the ABC triangle. points N, P, K – points of tangency, AB = 14 cm

A circle is inscribed in the ABC triangle. points N, P, K – points of tangency, AB = 14 cm, AN = 6, KC = 7. Find the perimeter of the triangle ABC.

From the center of the circle, point O, draw the radii OK, OН and OM to the points of tangency.

By the property of a tangent drawn from one point, the segments of the tangents are equal. Then AM = AН = 6 cm, CН = CK 7 cm, BK = BM.

Then the side length AC = AН + CН = 6 + 7 = 13 cm.

The length of the segment BM = AB – AM = 14 – 6 = 8 cm.

Then BK = BM = 8 cm.

Side length BC = ВK + СK = 8 + 7 = 15 cm.

Let’s define the perimeter of the triangle ABC.

Ravs = AB + BC + AC = 14 + 15 + 13 = 42cm.

Answer: The perimeter of the triangle is 42 cm.