segments ab and bc and ca are all tangent to the circle find the perimeter of triangle abc

Answer 1

If all three segments AB, BC, and CA are tangent to the circle, then triangle ABC is an isosceles triangle where AB = BC = CA.

Let r be the radius of the circle. Since each segment is tangent to the circle, we have that AB = BC = CA = r.

The perimeter of triangle ABC is the sum of the lengths of its sides:

Perimeter = AB + BC + CA = r + r + r = 3r

Therefore, the perimeter of triangle ABC is 3 times the radius of the circle.