Question

The chord of contact of tangents from a point 'P' to a circle passes through Q. If $l_{1}and{l}_2$ are the lengths of the tangents from P and Q to the circle, then PQ is equal to

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$P=(x_1,y_1)and(x_2,y_2)$ From P tangent to the given circle is $x{x}_1+y{y}_1=a^2$ Since it passes through $Q(x_2,y_2)$
$\therefore x_1{x}_2+y_1{y}_2=a^2\to \left(1\right)$
Now, $l_1=\sqrt{x_1^2+y_1^2-a^2},l_2=\sqrt{x_2^2+y_2^2-a^2}$ and
$PQ=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$ $i.e\sqrt{l_1^2+l_2^2}$