<p>If <span class="math">\(r_1 = r + r_2 + r_3\)</span>, then the triangle is</p>
Step-by-Step Solution
Key Concept: Apply the formulas for exradii and inradius in terms of area and semi-perimeter to determine what special property this equality implies.
<p>Using the relations <span class="math">\(r = \frac{\Delta}{s}\)</span>, <span class="math">\(r_1 = \frac{\Delta}{s-a}\)</span>, <span class="math">\(r_2 = \frac{\Delta}{s-b}\)</span>, <span class="math">\(r_3 = \frac{\Delta}{s-c}\)</span>, the condition <span class="math">\(r_1 = r + r_2 + r_3\)</span> simplifies to show that one angle equals 90°.</p><p>∴ Answer is (c) right angled.</p>
Correct Answer: C