Question

A line meets the coordinate axis in A and B.
A circle is circumscribed about the triangle OAB. If the distances from A and B of the tangent to the circle at the origin be m and n then the diameter of the circle is –

• A. m (m + n)
• B. m + n
• C. n (m + n)
• D. m² + n²

Answer 1

Answer: (B)

m + n

Answer 2

Coordinates of A be (a, 0) and B (0, b). AOB is right angled triangle centre of the circumscribed circle is mid point $\left( \frac{a}{2},\frac{b}{2} \right)$ of AB

and radius OC = $\sqrt{\frac{a^{2}}{4} + \frac{b^{2}}{4}}$

equation of circle = x² + y² – ax – by = 0

AL and BM be the perpendicular from A and B on tangent at origin ax + by = 0

AL = $\left| \frac{a^{2}}{\sqrt{a^{2} + b^{2}}} \right|$ = m , BM = $\left| \frac{b^{2}}{\sqrt{a^{2} + b^{2}}} \right|$ = n

m + n = $\sqrt{a^{2} + b^{2}}$ = diameter of the circle.