Question

A line meets the co-ordinate axes in A and B. A circle is circumscribed about DOAB. If the distances from A and B of the tangent to the circle at the origin be m and n, then 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

Circumcentre of DOAB ŗ

Cirumradius =

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

equation of tangent at origin ax + by = 0

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

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