Q. 245.0( 6 Votes )

In Fig. 8, O is t

Answer :

We know that, tangent of the circle is perpendicular to the radius through the point of contact

OPT = 90o


Also, it is given in the question that:


OP = 5 cm


OT = 13 cm


Now, in right triangle OPT by using the Pythagoras theorem we have:


OP2 + PT2 = OT2


(5)2 + PT2 = (13)2


PT2 = 144



PT = 12 cm


As radius of the circle are equal to each other


OP = OQ = OE = 5 cm


Also, ET = OT – OE


= 13 – 5


= 8 cm


Let us now assume PA = x cm


AT = (12 – x) cm


We know that, tangents of a circle drawn from an external point are equal


PA = AE = x cm


Now, in right triangle Aet by using the Pythagoras theorem we have:


AE2 + ET2 = AT2


x2 + (8)2 = (12 – x)2


x2 + 64 = 144 + x2 – 24x


24x = 80



Now, AB = AE + EB


= AE + AE


= 2 × AE


= 2x


Putting the value of x, we get:




= 6.67 cm


Hence, the length of the AB will be 6.67 cm

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