ABC is a right-angled triangle with AB = 6 cm and BC = 8

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ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with centre O has been inscribed inside ∆ABC. The radius of the circle is

1. 1 cm
2. 2 cm
3. 3 cm
4. 4 cm

Correct Option: B

As per the given in question , we draw a figure right-angled triangle ABC in which inscribed inside a circle with centre O ,

AC = √AB² + BC²
AC = √6² + 8²
AC = √36 + 64
AC = √100 = 10 cm
OD = OE = OF = radii = r cm
∴ Area of [∆ AOB + ∆ BOC + ∆ AOC] = ∆ABC

⇒	1	× 6 × r +	1	× 8 × r +	1	× 10 × r =	1	× 8 × 6
	2		2		2		2

⇒ 3r + 4r + 5r = 24
⇒ 12r = 24

⇒ r =	24	= 12 cm.
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