Question

ABC is a right triangle right angled at A . Circle is inscribed in it . The lengths of two sides containing the right angles are 6cm and 8cm . Find the radius of the incircle

Answer 1

Given: ΔABC is a right triangle , right angled at A . he lengths of two sides containing the right angles are 6 cm and 8 cm.

To find: The radius of incircle

Step-by-step explanation:

Now as Δ ABC is a right angled triangle therefore It follows Pythagoras theorem which states that the sum of squares of two sides of a right angle triangle is equal to the square of hypotenuse side

So we have

$BC^2=AB^2+AC^2\\\\\Rightarrow BC^2= 6^2+8^2\\\\\Rightarrow BC^2= 100\\\\\Rightarrow BC = 10cm$

Now

$\text {Inradius} =\dfrac{\text {Sum of two sides }-\text {Hypotenuse}}{2} = \dfrac{6+8-10}{2} =2$

Hence , the radius of incircle is 2 cm

Answer 2

Answer:

Answer is 2cm

Step-by-step explanation:

In triangle ABC by Pythagoras theorem,

BC² = AB²+AC²

BC²= 8²+6²

BC²=  100

BC= √100

BC= 10cm

From figure, ar(ABC)= ar(OBC)+ ar(OAB)+ ar(OCA)

$\frac{1}{2}$(8) (r)+ $\frac{1}{2}$ (10) (r)+ $\frac{1}{2}$ (6) (r)

24= $\frac{1}{2}$ [24 r]

$\frac{1}{2}$= r

r= 2cm