Question

In the given figure, O is the centre of two concentric circles for radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm. Find the length of BP.

Answer 1

Given that,
OA = 5 cm, OB = 3 cm and PA = 12 cm.

We know that,
Tangent drawn from any point outside the circle to point on the circle is perpendiuclar to the raidus.

Therefore, In triangle AOP angle A is right angle.

Now, applying pythagoras theorem

$O{A}^2+A{P}^2=O{P}^2$

$5^2+{12}^2=O{P}^2$

$13cm=OP$

Similarly, in triangle OBP angle B is right angle

Now, applying pythagoras theorem

$O{B}^2+B{P}^2=A{P}^2$

$9+B{P}^2=169$

$B{P}^2=160$

$BP=\sqrt{1}60cm$

$BP=4\sqrt{1}0cm$