Question

The point P is on circle $x^2+y^2=36$ and tangents are drawn to the circle $x^2+y^2=18$ from P. The angle between the tangent lines is

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (D)

${90}^{\circ }$

If drawn tangents from a point on the circle $x^2+y^2=36$ onto the circle $x^2+y^2=18$, we find that if $\theta$ is the angle made by the tangent with the line joining the point from which tangents are drawn and the centre of the circles, $\sin \theta =\frac{\sqrt{18}}{\sqrt{36}}=\frac{1}{\sqrt{2}}$

This implies that $\theta$ is ${45}^o$.

$\Rightarrow$ that the tangents make an angle of $2\theta$, i.e. ${90}^o.$