Circles
RD Sharma
CBSE
Grade 10
Question:
In a right triangle $ABC$ right-angled at $B$, $AB = 5\text{ cm}$ and $BC = 12\text{ cm}$. Find the radius of the circle inscribed in the triangle.
Step-by-Step Solution
Key Concept: $AC = \sqrt{25 + 144} = 13\text{ cm}$. Inradius $r = \dfrac{a + b - c}{2} = \dfrac{5 + 12 - 13}{2} = \dfrac{4}{2} = 2\text{ cm}$.
Hypotenuse $AC = 13\text{ cm}$. [0.5 Mark]
Inradius $r = \dfrac{5 + 12 - 13}{2} = 2\text{ cm}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Finding hypotenuse $= 13\text{ cm}$: 0.5 Mark
Evaluating inradius $r = 2\text{ cm}$: 1.5 Marks
Correct Answer:
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