Direct common tangent between two circles:\nThe distance between the centres is 61 cm, and the radii are 35 cm and 24 cm. Find the length (in cm) of a direct common tangent.

Introduction / Context:
For two non-overlapping circles, the length of a direct common tangent segment depends on the centre distance and the difference of the radii via the Pythagorean relation from the right triangle formed by centres and tangent points.

Given Data / Assumptions:

• Centre distance d = 61 cm.
• Radii r1 = 35 cm, r2 = 24 cm.

Concept / Approach:
Direct tangent length L satisfies L^2 = d^2 − (r1 − r2)^2.

Step-by-Step Solution:

Verification / Alternative check:
The circles are externally disjoint since 61 > 35 + 24 = 59; tangent length is real and positive.

Why Other Options Are Wrong:
54, 48, 72, 50 do not satisfy L^2 = 3600.

Common Pitfalls:
Using r1 + r2 instead of r1 − r2 (that formula is for the transverse/common internal tangent relation when needed).

Final Answer:
60