A line meets the coordinate axes in A and B. A circle is circumscribed about the △AOB. If m,n are the distance of the tangent to the circle at the origin from the points A and B, respectively the diameter of the circle is
A
m(m+n)
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B
m+n
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C
n(m+n)
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D
None of these
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Solution
The correct option is Am+n Let A≡(a,0) and B≡(0,b)
Since ∠AOB=900, ∴AB is the diameter
∴ Center of the circle is and radius =12√a2+b2.
∴ Equation of the circle is
(x−a2)2+(y−b2)2=14(a2+b2)⇒x2+y2−ax−by=0
Equation of tangent to the circle at O(0,0) is ax+by=0 ...(1)