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.
Explain with the diagram
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