﻿ A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is : Kaysons Education

# A Line Meets The Coordinate Axes In A and B. A Circle Is Circumscribed About The Triangle OAB. If m and n are The Distances Of The Tangent To The Circle At The Origin From The Points A and B respectively, The Diameter Of The Circle Is

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## Question

### Solution

Correct option is

m + n

Let the coordinates of A be (a, 0) and that of B be (0, b) (Fig). Since∠AOB = π/2, the line AB is a diameter of the circle circumscribing the triangle OAB, its centre is mid-point of AB, i.e., (a/2, b/2), and its radius is (1/2)  Therefore, equation of the circle throughOA and B is

x2 + y2 – ax – by = 0, and the equation of the tangent at the origin to this circle is ax + by = 0. If AL and BM are the perpendicular from A and B to this tangent, then

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