The distance between the centres of two circles is 24 cm. If the radius of the two circles are 4 cm and 8 cm, then what is the sum of the lengths (in cm) of the direct common tangent and the transverse common tangent?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 4(√35 + 3√3)
Length of the direct common tangent
= √[d2 – (r1 – r2)2]
= √[242 – (8 – 4)2]
= √[576 – 16]
= √560
= 4√35 cm
and Length of the transverse common tangent
= √[d2 – (r1 + r2)2]
= √[242 – (8 + 4)2]
= √[576 – 144]
= √432
= 12√3 cm
Hence, Sum = 4√35 + 12√3
= 4(√35 + 3√3) cm