A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/6 #, and the triangle's area is #4 #. What is the area of the triangle's incircle?

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Answer 1 · 2016-10-01T19:22:49

#pir² ~~ 1.07#

Given:

#Delta = 4# where #Delta# is the area of the triangle.
#A = pi/12#
#B = pi/6#

We can compute the measure of angle C:

#C = pi - A - B = 3pi/4#

Using a equation from the source

#Delta = r²(cot(A/2) + cot(B/2) + cot(C/2))#

The area of the incircle is #pir²#

#pir² = piDelta/(cot(A/2) + cot(B/2) + cot(C/2))#

#pir² ~~ 1.07#