Two circles of radii 16 cm and 4 cm, respectively, touch each other externally at Point A. PQ is the direct common tangent of these circles with centres C1 and C2 , respectively. What is the length of PQ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 16 cm.
The radius of Circle 1 (r1) = 16 cm
The radius of Circle 2 (r2) = 4 cm
Length of direct common tangent = √(Distance between centres2 - Difference between radius of two circles2)
Distance between centres (d) = r1 + r2 = 16 + 4 = 20 cm
Difference between the radius of two circles = 16 - 4 = 12 cm
Now, PQ = √(202 - 122) = √(400 - 144) = √256 = 16 cm
Therefore, the length of PQ is 16 cm.