The angle between the tangents drawn at the points `(5,12)` and `(12,-5)` to the circle `x^2+y^2=169` is:

Explanation

`x^2+ y^2=169`

Differentiating w.r.t x

`2x+ 2ydy/dx=0`

`dy/dx= -x/y`

`dy/dx at (5,12)=-5/12=m1`

`dy/dx at (12,-5)= 12/5=m2`

As, `m1*m2=(-5/12)(12/5)=-1`
So, Angle between tangents= `pi/2`