A circle is inscribed in an isosceles triangle, in which the side is 100 and the base is 60.

A circle is inscribed in an isosceles triangle, in which the side is 100 and the base is 60. Find the distance between the swing points on the sides.

Let’s build the points of tangency K, M, H of the circle and the triangle. Since the triangle is isosceles, the point of contact H is the middle of the AC side, AH = CH = AC / 2 = 60/2 – 30 cm.

By the property of tangents drawn from one point, AK = AK = 530 cm, CM = CH = 30 cm.

Then BK = BM = 100 – 30 = 70 cm.

Since AK = CM, then KM is parallel to AC, then triangles ABC and BKM are similar in two angles.

The coefficient of similarity of triangles is: K = BK / AB = 70/100 = 7/10.

Then KM = AC * 7/10 = 60 * 7/10 = 42 cm.

Answer: Between touching points 42 cm.