A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. The distances from the end points A, B of the side AB to the tangent at O are equal to m and n respectively. Then, the diameter of the circle, is

Question

A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. The distances from the end points A, B of the side AB to the tangent at O are equal to m and n respectively. Then, the diameter of the circle, is

Infinity Learn · Accepted Answer

Let the coordinates of A and B be (a$$, $$0) and (0$$, $$b) respectively. Since the triangle OAB is a right angled triangle, the centre of the circumcircle is the mid point of AB i.e. (a/2$$,$$b/2) and the radius is equal to $$12AB=12a2+b2The$$ equation of the circumcircle is $$x2+y2$$−ax−$$by=0The$$ equation of the tangent at the origin to this circle is $$ax+by=0$$.∴ $$m=a2a2+b2$$ and $$n=b2a2+b2$$⇒ $$m+n=a2+b2=$$ Diameter of the circle.

Definition of a circle

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A line meets the coordinate axes in $A$ and $B .$ $A$ circle is circumscribed about the triangle $O A B .$ The distances from the end points $A, B$ of the side AB to the tangent at $O$ are equal to $m$ and $n$ respectively. Then, the diameter of the circle, is

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