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Three circles, whose radii are a,b,c touch each other externally and the tangents at their points of contact meet in a point. Then, the distance of this point from either point of contact is:
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\sqrt{\frac{abc}{a + b + c}}

\sqrt{\frac{abc}{a - b - c}}

2 \sqrt{\frac{abc}{a + b + c}}

None of these.

answer is A.

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Detailed Solution

Let ID,IE,IF be the common tangents meeting at I.
Then ID =IF and IE=IF
∴ID =IE=IF
Since ID⊥BC,IE⊥CA,IF⊥AB
∴I is the incentre of ΔABC whose side are b+c,c+a,a+b
Now 2s=b+c+c+a+a+b=2(a+b+c)
∴s=a+b+c

Δ = \sqrt{s (s - \underset{̲}{b + c}) (s - \underset{̲}{c + a}) (s - \underset{̲}{a + b}) = \sqrt{s (a) (b) (c)} = \sqrt{sabc}}

Now

r = \frac{Δ}{s} = \frac{\sqrt{sabc}}{s} = \sqrt{\frac{abc}{s}} = \sqrt{\frac{abc}{a + b + c}}

Type Exam: CBSE

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