Challenging Geometry Problem 1609. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.
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Very straightforward and obvious solution
ReplyDeleteLet O be the centre of the semi-circle
Let S(ABC) = S
Then S = S(AOB) + S(COB) = rc/2 + ra/2
Hence S = r(a+c)/2 and r = 2S/(a+c) .......(1)
But S = V{s(s-a)(s-b)(s-c) ....... (2) as is well known
The required result follows easily from (1) and (2)
Sumith Peiris
Moratuwa
Sri Lanka