Question

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of $25cm$ from O as shown in the figure. The radius of the circle with centre O is $7cm$. The diameter of the circle with centre O’ is $10cm.$ What is the length of the tangent PC?

• A. $26cm$
• B. $24cm$
• C. $27cm$
• D. $25cm$

Answer 1

The correct option is B

$24cm$

In the given figure, $PO=25cm$ and $OA=7cm$
We know that the tangent is perpendicular to the radius at the point of contact
So, $\angle POA={90}^{\circ }.$
Hence, applying pythagoras theorem, we have $P{O}^2=A{O}^2+P{A}^2$
${25}^2=7^2+P{A}^2$
Hence, $P{A}^2=625-49=576$
$\Rightarrow PA=24cm$
Now, considering the circle with centre O' alone



We know that $PA=24cm.$ Now PA and PC are tangents from an external point P to the same circle. Hence, they are equal in length.
Thus, $PC=PA=24cm.$