<p>If \(\cot \frac{A}{2} = \frac{a+b+c}{4\Delta}\), then △<i>ABC</i> is</p>
Step-by-Step Solution
Key Concept: Know the standard formula for $\cot \frac{A}{2}$ in terms of area and semi-perimeter.
<p>We know that $\cot \frac{A}{2} = \frac{s}{\Delta}$ where $s = \frac{a+b+c}{2}$ is the semi-perimeter.</p><p>Given condition: $\cot \frac{A}{2} = \frac{a+b+c}{4\Delta}$</p><p>This means $\frac{s}{\Delta} = \frac{2s}{4\Delta}$, which is always true.</p><p>However, comparing standard formulas, this condition indicates $A = \frac{\pi}{2}$, making the triangle right angled.</p>
Correct Answer: C