A and B are centers of two circles of radii 32 cm and 8 cm, respectively. CD is a direct common tangent to the circles. If the length of AB = 30 cm, then the length of CD will be:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 18 cm.
Given,
Radius1 = r1 = 32 cm
Radius2 = r2 = 8 cm
Distance between the centers of the two circles = d = 30 cm
We know,
Length of direct common tangent = √(d2 - (r1 - r2)2)
According to the question;
⇒ Length of direct common tangent = CD = √(302 - (32 - 8)2)
⇒ √(900 - 576)
⇒ √324
⇒ 18 cm