Question 536449
Find the area of the triangle formed by the 3 centers using Heron's Law.
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Find the 3 angles at the centers.
Use the Cosine Law for 1, then either the Cosine Law or the Law of Sines for the 2nd, then 180 - (sum of 1st 2) for the 3rd.
Find the 3 radii:
r1 + r2 = 25
r1 + r3 = 20
r2 + r3 = 23
--> 9, 11 & 14 for radii
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Find the area of each sector, add them, and subtract from the area of the triangle.