# pre calc

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each of three circles touches the other 2.circle A has a radius of 8 cm. circle B has a radius of 4 cm.circle C has a radius of 1 cm.a triangle is formed by connecting the centers of the 3 triangles. determine the largest angle for the triangle and in which circle is the largest angle?

• pre calc -

Draw a diagram. The sides of the triangle are 12,9,5

The angle at C subtends the longest side, so it will be the largest angle.

by the law of cosines,

12^2 = 9^2 + 5^2 - 2*9*5 cosC
144 = 81 + 25 - 90 cosC
cosC = -38/90
C = 115°

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