Two circles have centers M and N with radii 10 cm and 6 cm, respectively. The distance MN is 13 cm. QR is a common external tangent to both circles. What is the length of QR? (the segment between the points of tangency)
Show answer & explanation
Correct answer: C
Explanation
Given:
r₁ = 10 cm, r₂ = 6 cm
MN = 13 cm
According to the formula:
Length of the internal/external tangent = √[MN² − (r₁ − r₂)²]
= √[13² − (10 − 6)²]
= √[169 − 16]
= √153
= √(9 × 17)
= 3√17 cm