Question

P and Q are 2 external points from which tangents are drawn to circle centered at origin and radius 'r' $P\equiv (x_1,y_1),Q\equiv (x_2,y_2).$ What is the condition for the lengths of tangents to be the same?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

This becomes easy to solve when we employ the equation for the length of tangent length of tangent

from a point $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $\sqrt{S_1}$ where $S_1$ is the expression we get on replacing $x$ by $x_1$ and

$y$ by $y_1$.

$\therefore$ since length of tangents are equal

$\sqrt{S_1}=\sqrt{S_2}$

$i.e.,\sqrt{x_1^2+y_1^2-r^2}=\sqrt{x_2^2+y_2^2-r^2}$