# A circle is inscribed in a triangle with angles of 50 and 70. find the corners of a triangle whose

**A circle is inscribed in a triangle with angles of 50 and 70. find the corners of a triangle whose vertices are the points of tangency of the circle with the sides of the triangle**

Let’s denote this triangle ABC, angle A = 50 °, angle B = 70 ° of the point of tangency of the circle:

H with side AB;

To the side of the aircraft;

M with AC side.

The third corner of the triangle is:

∠ С = 180 ° – (50 ° + 70 °) = 60 °.

The property of tangents drawn from one point allows us to select three isosceles triangles: AСM, ВНK, СMK.

Find the angles at the base of these triangles:

∠ АНМ = ∠ АМН = (180 ° – 50 °) / 2 = 65 °;

∠ ВKН = ∠ ВKН = (180 ° – 70 °) / 2 = 55 °;

∠ СMK = ∠ CКM = (180 ° – 60 °) / 2 = 60 °.

Find the angles of the НKM triangle:

∠ Н = 180 ° – 65 ° – 55 ° = 60 °;

∠ К = 180 ° – 55 ° – 60 ° = 65 °;

∠ M = 180 ° – 60 ° – 65 ° = 55 °.

Answer: 60 °, 65 °, 55 °.