Question

∆LMN is a right angled triangle with L = 90°. A circle is inscribed in it. The
lengths of the sides containing the right angle are 6 cm and 8 cm. Find the radius of
the circle.​

Answer 1

The radius of circle=2cm

Step-by-step explanation:

Let a=6cm and b=8cm

Using Pythagoras theorem

$(Hypotenuse)^2=(Perpendicular\;side)^2+(base)^2$

$c^2=6^2+8^2=36+64$

$c^2=100$

$c=\sqrt{100}=10cm$

Area of triangle LMN=$\frac{1}{2}\times base\times height$

Area of triangle LMN=$\frac{1}{2}\times 6\times 8=24cm^2$

Semi-perimeter of triangle LMN=$\frac{8+6+10}{2}=12cm$

Radius of circle=$\frac{area\;of\;triangle}{semi-perimeter\;of;triangle}$

Radius of circle=$\frac{24}{12}=2cm$

Hence, the radius of circle=2cm

#Learns more:

https://brainly.in/question/2637168:Answered by Sivamammu