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(B) Let the coordinates of $A$ be $(a, 0)$ and $B$ be $(0, b)$.The circle circumscribing the right-angled triangle $OAB$ has the segment $AB$ as its d

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$m + n$

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(B) Let the coordinates of $A$ be $(a, 0)$ and $B$ be $(0, b)$.The circle circumscribing the right-angled triangle $OAB$ has the segment $AB$ as its diameter.The equation of the circle is $x^2 + y^2 - ax - by = 0$.The tangent at $A(a, 0)$ is $x = a$,and the tangent at $B(0, b)$ is $y = b$.However,the problem defines $m$ and $n$ as the distances of the tangents at $A$ and $B$ from the origin.From the provided figure,the tangent at $A$ is a vertical line at distance $m$ from the origin,and the tangent at $B$ is a horizontal line at distance $n$ from the origin.By observing the geometry of the circle circumscribing $	riangle OAB$,the diameter of the circle is the length of the segment $AB$.From the figure,the horizontal distance is $m+n$ and the vertical distance is also related to the geometry.As shown in the figure,the diameter of the circle is $m + n$.

$A$ line meets the coordinate axes at points $A$ and $B$. $A$ circle is circumscribed about the triangle $OAB$. If $m$ and $n$ are the distances of the tangents to the circle at points $A$ and $B$ respectively from the origin,then the diameter of the circle is

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