If two equal circles of radius 5 cm have two common tangents AB and CD which touch the circles at point A, B, C and D. If CD = 18 cm then find the length of AB.?

Option 2 : 20.59 cm

Let the distance between both circle be x cm.

CD is a transverse common tangent between the two circles

Length of direct transverse tangents = (square of distance between the circle – square of sum radius of the circle)^1/2

⇒ CD = {(x)² – (5 + 5)²}^1/2

⇒ 18 = {(x)² – (10)²}^1/2

⇒ 324 = {(x)² – 100}

⇒ (x)² = 324 + 100 = 424

⇒ (x) = 20.59

Length of direct common tangents = (square of distance between the circle – square of difference between radius of the circle)^1/2

AB is the direct common tangents between first and second circle

⇒ AB = {(20.59)² – (5 − 5)²}^1/2

⇒ AB = {(20.59)²}^1/2