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For a triangle of sides a, b, c and area A, the incircle radius r equals:
Answer & Solution
Correct answer: D.
1. Join the incentre to each vertex, splitting the triangle into three small triangles.
2. Each small triangle has height r (perpendicular distance from incentre to that side).
3. Their areas sum to (1/2)(ar + br + cr) = (1/2)(a + b + c)r = sr.
4. This total equals A, the area of the triangle.
5. Hence r = A/s.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7-8 (pp 180-199, 2019 ed.)._
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