Q. 75.0( 5 Votes )

In Fig. 10.58, there are two concentric circles with centre O of radii 5 cm and 3 cm. from an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.


Answer :

Given: OA = 5 cm


OB = 3 cm


AP = 12 cm


To find: The length of BP.


Theorem Used:


1)Tangent to a circle at a point is perpendicular to the radius through the point of contact.


2) Pythagoras theorem:


In a right-angled triangle, the squares of the hypotenuse is equal to the sum of the squares of the other two sides.


Explanation:



PA and PB are the tangent drawn from the external point A and B to the radius OA and OB.


From the theorem (1) stated above,


OAP = 90°


OBP = 90°



OA=5cm, OB=3cmandAP=12cm
In
OAP by the theorem (2),


OP2 = OA2 + AP2


OP2 = 52 + 122


OP2 = 25 + 144


OP2 = 169


OP = √169


OP = 13 cm


In OBP by the theorem (2),


OP2 = PB2 + OB2


132 = PB2 + 32


169 = PB2 + 9


160 = PB2




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