Two circles, one with a radius of 13 cm and the other with a radius of 5 cm, have their centers 20 cm apart. A direct common tangent is drawn between the two circles. What is the length of this tangent?
Show answer & explanation
Correct answer: C
Explanation
Given:
R₁ = 13 cm
R₂ = 5 cm
Distance between centers (d) = 20 cm
Formula:
Length of the direct common tangent = √(d² − (R₁ − R₂)²)
= √(20² − (13 − 5)²)
= √(400 − 8²)
= √(400 − 64)
= √336
= 4√21 cm