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  4. A circle C1 has radius 2 units and a circle C2 has radius 3 units. The distance between the centres of C1 and C2 is 7 units. If two lines, one tangent to both circles and the other passing through the center of both circles, intersect at point P which lies between the centers of C1 and C2 , then the distance between P and the centre of C2 is

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Q. A circle $C_{1}$ has radius $2$ units and a circle $C_{2}$ has radius $3$ units. The distance between the centres of $C_{1}$ and $C_{2}$ is $7$ units. If two lines, one tangent to both circles and the other passing through the center of both circles, intersect at point $P$ which lies between the centers of $C_{1}$ and $C_{2}$ , then the distance between $P$ and the centre of $C_{2}$ is

NTA AbhyasNTA Abhyas 2020Conic Sections

Solution:

Solution
Since $\triangle O_{1}PT_{1}\sim \triangle O_{2}PT_{2}$ ,
$\therefore \frac{2}{3}=\frac{x}{7 - x}$
$3x=14-2x$
$x=\frac{14}{5}$
$\Rightarrow PO_{2}=7-\frac{14}{5}=\frac{21}{5}$ units