Question

If a right angled triangle ABC of maximum area is inscribed with in a circle of radius R,then​

​

Answer 1

Answer:

Step-by-step explanation:

For a right-angled triangle inscribed in a circle of radius R, the length of the hypotenuse is 2R

∴ the area is maximum when the triangle is isosceles with each side =  

2

​  

R

∴s=  

2

1

​  

(2  

2

​  

+2)R=(  

2

​  

+1)R

∴△=  

2

1

​  

 

2

​  

R.  

2

​  

R=R  

2

⇒  

r

1

​  

=  

R

(  

2

​  

+1)

​  

 

∴  

r  

1

​  

 

1

​  

+  

r  

2

​  

 

1

​  

+  

r  

3

​  

 

1

​  

=  

△

s−a

​  

+  

△

s−b

​  

+  

△

s−c

​  

=  

△

s

​  

=  

r

1

​  

=  

R

(  

2

​  

+1)

​