Question

Three circles are described touching each other at two places externally. If the sides of triangle are 4 cm,6 cm, and 8 cm.Find the radii of the circles.

Answer 1

let the three circles have centers at A, B and C. The triangle formed by the centers be ABC. Let the radii of the circles be r1, r2 and r3.
AB = r1 + r2   = 4 cm (circles touch externally
BC = r2 + r3  = 6 cm
CA = r3 + r1   = 8 cm

Add all these :   2 (AB + BC + CA) = 18 cm
AB+ BC + CA = 9 cm

Subtracting each of the three equations frm the above eq.  we get:
        r3 = 5 cm          r1 = 3 cm              r2 = 1 cm

Answer 2

Answer:

Step-by-step explanation

radius is 5 , 3 , 1