A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius…

CBSE Class 10 Maths PYQ · Circles · Triangle & Circle · 3 Marks · March 2024 · Standard

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953 Marks · March 2024 · Standard

A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = $7$ cm and AB = $24$ cm, find the radius of the circle.

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$AC = \sqrt{24^2 + 7^2} = 25$ cm
Let the radius of the circle be '$r$' cm
$$\begin{aligned}& \frac{1}{2} \times 24 \times 7 = \frac{1}{2} \times r \times 7 + \frac{1}{2} \times r \times 24 + \frac{1}{2} \times r \times 25 \\ & \Rightarrow r = 3 \\ & \therefore\end{aligned}$$ radius of circle is $3$ cm.