Three circles with radii of 4, 5, and 6 cm, respectively, are tangent to each other externally. Find the angles of the triangle whose vertexes are the centers of the circles.

Answer 1

sides of triangle are (2+2.5),(2+3),(2.5+3)

Start with law of cosines

c^2=a^2+b^2-2abCosC

label the sides a,b, c solve for angle C
Then, use the law of sines
a/SinA=c/SinC solve for angle A
then use the fact that the sum of the angles is 180 deg, find angle B.
check angle B with the law of sines.

Answer 2

474