AB and CD are two common tangents to circles which touch each other at C. If D lies on AB such that CD = 4 cm, then find the length of AB.

4 cm

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6 cm

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8 cm

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12 cm

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Solution

The correct option is C
8 cm

Given that CD = 4 cm

We know that CD = DB (tangents from an external point to a circle are equal)

Therefore DB = 4 cm

Also AD = DC (tangents from an external point to a circle are equal)

Therefore AD = 4 cm

Now AB = AD + DB = 4 + 4 = 8 cm

Therefore, the length of AB is 8 cm.

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Similar questions

Q. AB and CD are two common tangents to circles which touch each other at C. If D lies on AB such that CD = 4 cm, then AB is equal to

(a) 4 cm

(b) 6 cm

(c) 8 cm

(d) 12 cm

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .

In the following figure, if the chords AB and CD are equal to 6cm, then find the distance of the chords AB and CD from the centre of the circle of radius 5 cm.

AB and CD are two equal chords of a circle. If chord AB is at a distance of 4 cm from the centre, then the distance of chord CD from the centre is

A B

and

C D

are two chords of a circle which intersect each other internally at

P

(i) If

C P = 4 c m, A P = 8 c m, P B = 2 c m

, then find

P D

.
(ii) If

A P = 12 c m, A B = 15 c m, C P = P D

, then find

C D

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