In two circles centered at O and O’, the distance between the centres of both circles is 17 cm. The points of contact of a direct common tangent between the circles are P and Q. If the radii of both circles are 7 cm and 15 cm, respectively, then the length of PQ is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 15 cm.
Given that
The distance between the centers of both circles is d = 17 cm.
The points of contact of a direct common tangent between the circles are P and Q
The radius of big circle (R) = 15 cm
The radius of a small circle (r) = 7 cm
According to the question
Direct common tangent = √[d2–(R – r)2]
Calculation
DCT = √[172–(15 – 7)2]
= √[289– 64] = √225 = 15 cm