2 circles touch each other externally at C. AB and CD are 2 common tangents. If D lies on AB such that CD=6cm, then find AB.
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Solution

Given, two circles touch each other externally at C and AB and CD are two common tangents such that D lies on AB.

It is known that the length of tangents drawn from an exterior point to a circle arc of equal length

∴ AD = CD and BD = CD ... (1)

Given, CD = 6 cm

Also, AB = AD + DB

⇒ AB = CD + CD [using (1)]

⇒ AB = 6 + 6 = 12 cm

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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.

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