Two externally touching circles\nTwo circles touch externally. The distance between their centres is 12 cm. If the radius of one circle is 7 cm, find the diameter (in cm) of the other circle.

Introduction / Context:
When circles touch externally, the distance between centres equals the sum of their radii. From that, we can find the unknown radius and then the diameter (twice the radius).

Given Data / Assumptions:

• Distance between centres = 12 cm
• Known radius r1 = 7 cm
• Let unknown radius r2 be required; diameter sought is 2 * r2.

Concept / Approach:
Externally touching ⇒ r1 + r2 = distance. Solve for r2, then compute 2r2 for the diameter.

Step-by-Step Solution:

Verification / Alternative check:
Substitute back: 7 + 5 = 12 (equals given centre distance), so the configuration is consistent.

Why Other Options Are Wrong:
12 is the centre distance, not the diameter; 8 and 5 do not reflect the computed diameter; only 10 cm fits.

Common Pitfalls:
Confusing external with internal touching (where distance is the absolute difference of radii) changes the equation entirely.

Final Answer:
10