Geometry Problem 1546. Post your solution in the comment box below.

Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Reference my solution to Problem 80,

ReplyDeleteArea of the Contact Circle = S. r^2 (1/ab + 1/bc + 1/ca)

= S.(S/s)^2 . (2s)/abc

= 2S^3 / (sabc) ............(1)

Now s = (7+8+9)/2 = 12

S = V{s(s-a)(s-b)(s-c)} = V(12 X 5 X 4 X 3) = 12. V5

Hence from (1) Area of the Contact Circle

= 2. 12^3 . 5^(3/2) / (12 X 7 X 8 X 9)

= 6.4 approximately

Sumith Peiris

Moratuwa

Sri Lanka