Geometry Problem 1545. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.
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Let s = semiperimeter and S the area of Triangle ABC
ReplyDeleteWith the usual notation exradius rA = S /(s-a), BE = s-b
Hence S(BEH) = (1/2)(S/(s-a))(s-b) = 11 so
(s-b)/(s-a) = 22/S
Simlarly (s-a)/(s-c) = 20/S and
(s-c)/(s-b) = 12/S
Multiplying, 1 = 22 X 20 X 12 / (S^3)
Hence S = 2.(660)^(1/3) = 17.41 approximately
Sumith Peiris
Moratuwa
Sri Lanka