A common internal tangent is drawn to two circles with radii 4 and 9 units. If the length of the tangent segment is 12 units, what is the distance between the centers of the two circles?
Show answer & explanation
Correct answer: D
Explanation
Given:
Radius of the first circle = 4
Radius of the second circle = 9
Length of the internal tangent segment = 12
Formula:
For the internal tangent,
Tangent segment² = d² − (r₁ + r₂)²
12² = d² − (4 + 9)²
144 = d² − 13²
144 = d² − 169
d² = 144 + 169
d² = 313
d = √313 units