The radii r1,r2,r3 of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24cm2 and its perimeter is 24cm, the the length of its largest side is
A
10
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B
9
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C
8
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D
none of these
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Solution
The correct option is A10 Since, r1,r2,r3 are in H.P Therefore, 2r2=1r1+1r3 ⇒2(s−b)△=(s−a)△+(s−c)△ ⇒2b=a+c Given that, 2s=a+b+c=24 ⇒3b=24 ⇒b=8 and a+c=16....(1) Now, △2=s(s−a)(s−b)(s−c) 242=12(12−a)(12−8)(12−c) ⇒48=(a−4)(12−a) [ from (1) ] ⇒a2−16a+60 ⇒a=6,10 Ans: A