Circumradius of a right triangle with sides 9 cm, 12 cm, 15 cm: Find the circumradius (radius of the circumscribed circle) of the triangle.

Introduction / Context:For a right triangle, the circumradius equals half the hypotenuse. Recognizing the Pythagorean triple (9, 12, 15) streamlines the answer.

Given Data / Assumptions:

• Sides: 9, 12, 15 cm (hypotenuse = 15 cm).

Concept / Approach:In a right triangle, the circumcenter is the midpoint of the hypotenuse; hence R = hypotenuse / 2.

Step-by-Step Solution:

Verification / Alternative check:General formula R = (abc) / (4Δ). With a = 9, b = 12, c = 15 and Δ = (1/2)*9*12 = 54: R = (9*12*15)/(4*54) = 1620/216 = 7.5 cm.

Why Other Options Are Wrong:6 cm, 4.5 cm, 8 cm, 5 cm do not equal half the hypotenuse.

Common Pitfalls:Using inradius formula or confusing circumradius with the radius of the incircle.

Final Answer:7.5 cm