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Circles
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10
Question:
[Section C]
A circle is inscribed in a right-angled triangle $ABC$, right-angled at $B$. If $AB = 3$ cm and $BC = 4$ cm, find the radius $r$ of the circle.
A circle is inscribed in a right-angled triangle $ABC$, right-angled at $B$. If $AB = 3$ cm and $BC = 4$ cm, find the radius $r$ of the circle.
Step-by-Step Solution
Key Concept: Hypotenuse $AC = 5$ cm. Radius $r = \dfrac{a + b - c}{2} = \dfrac{3 + 4 - 5}{2} = 1$ cm.
$AC = \sqrt{3^2 + 4^2} = 5$ cm. $\text{Area}(\Delta ABC) = \dfrac{1}{2} \times 3 \times 4 = 6$ cm$^2$. Also $\text{Area} = r \times s = r \times \dfrac{3+4+5}{2} = 6r$. Thus $6r = 6 \Rightarrow r = 1$ cm. [3.0 Marks]
Correct Answer: r = 1 cm
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