Multiple choice

A line meets the co-ordinate axes in A & B. A circle is circumscribed about the $\triangle \ OAB$ . If 6 & 3 are the distances of the tangent to the circle at the origin O from the points A and B respectively, the diameter of the circle is

  1. $\frac{15}{2}$

  2. 6

  3. 2

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the line be x/a + y/b = 1. The distance from origin to the line is h = 1/sqrt(1/a^2 + 1/b^2). The tangent distances are related to the intercepts. Using geometry of the circumcircle of the right triangle OAB, the diameter is the hypotenuse AB = sqrt(a^2 + b^2). Given the tangent distances 6 and 3, the diameter is 9.

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