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Question

AB and BC are the tangents to the circle from the points B. D is the centre of the circle. BD = 5 cm and CD = 3 cm. Find the value of AB - BC.


A

20 cm

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B

4 cm

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C

9 cm

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D

0 cm

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Solution

The correct option is D

0 cm


In the above diagram,
AD = DC = 3 cm (Radius of the circle)

In ΔADB
AD = 3 cm (Radius of the given circle)
DB = 5 cm (Given)

DAB=90 (The tangent at any point of a circle and the radius through the point are perpendicular to each other)

(AB)2+(AD)2=(BD)2(AB)2+32=52(AB)2=259(AB)2=16
AB = 4

AB = BC = 4 (If two tangents are drawn to a circle from an exterior points, the tangents are equal in length)

AB - BC = 4 - 4 = 0 cm


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