Question

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is ______.

• A. 4 units
• B. 2 units
• C. 3 units
• D. 5 units

Hint:

While the general formula for the circumradius of any triangle is $R = \frac{abc}{4\Delta}$ (where $\Delta$ is the area), spotting a Pythagorean triple instantly reduces the calculation time to 3 seconds.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
First, check if the triangle is a right-angled triangle. A triangle with sides $a, b, c$ is right-angled if $a^2 + b^2 = c^2$.

Step 2: Formula Application:
$6^2 + 8^2 = 36 + 64 = 100 = 10^2$. Since it satisfies Pythagoras' theorem, it is a right-angled triangle with the hypotenuse equal to 10 units.

Step 3: Explanation:
For any right-angled triangle, the circumradius ($R$) is exactly half of the length of the hypotenuse. $R = \frac{\text{Hypotenuse}}{2} = \frac{10}{2} = 5$ units.

Step 4: Final Answer:
The circumradius is 5 units.