Multiple choice

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

  1. 4 cm

  2. 6 cm

  3. 8 cm

  4. 12 cm
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C Correct answer
Explanation

For two circles touching externally, the length of the common tangent segment between the points of contact is 2 * sqrt(R * r). The property of the common tangent segment AB where D is the point of contact on the tangent implies AB = 2 * CD = 2 * 4 = 8 cm.

AI explanation

Let the points of contact of the tangent from D with the two circles be A and C. By the property of tangents from an external point, DA equals DC, and similarly DB equals DC. Since CD = 4 cm, both DA and DC are 4 cm; thus, AB = DA + DB = 4 + 4 = 8 cm.

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