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 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10 cm. What is the length of the tangent PC?

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

Answer 1

The correct option is B 24 cm

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