If the pair of tangents drawn to the circle $x^2+y^2=a^2$ from the point $(10,4)$ are perpendicular, then $a=$

Question

Aicharya · Accepted Answer

Since the tangents are mutually perpendicular $\therefore \frac{\angle P}{2}=45^{\circ}$

Let the point of contact of the tangent and the circle be $A$ and $B$. Then in $\triangle P A C, P A=C A$ since the triangles are isoscles right angled triangle. $\begin{aligned} & P C=\sqrt{2} a \Rightarrow(P C)^2=2 a^2 \\ & \Rightarrow\left(10^2+4^2\right)=2 a^2 \Rightarrow a=\sqrt{58} \end{aligned}$

If the pair of tangents drawn to the circle $x^2+y^2=a^2$ from the point $(10,4)$ are perpendicular, then $a=$

Solution