Questions & Answers

Question

Answers

A.4 cm

B.6 cm

C.8 cm

D.12 cm

Answer
Verified

Let’s construct the diagram using the given information

According to the given information we have two circles which touch each other at point C also the circle have 2 common tangents AB and CD

And there is a point D which lie on AB such that CD = 4cm

So the constructed diagram is

To find the value of AB let join Point B and C and point A and C so the diagram we get is

As we know that the two tangent drawn from the same external point from the circle are equal in length

Therefore we can say that CD = DB

Since CD = DB so DB = 4 cm

Similarly for tangent AD and DC by the property of tangent from the same external point form circle

AD = CD

So AD = 4 cm

Since AB is equal to AD + DB i.e. AB = AD + DB

Substituting the given values in the above equation we get

AB = 4 cm + 4 cm

AB = 8 cm

Since the measure of AB is 8 cm.

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