Question

Q.15 In the image given below, if the radius of all the large circles is r, the
what is the radius of the inner smaller circle?/ नीचे दी गयी आकृति में यदि
बड़े वृत्त की त्रिज्या r है तो अंदर के छोटे वृत्त की त्रिज्या क्या है ?​

Answer 1

Answer:

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Step-by-step explanation:

Let the same radii of all four circles be 'r'

Let the inner circle radius be 'R'

Joining any two diagonally opposite circles center by a line passing through the center of inner circle, we get a diagonal for the square, a square is formed by joining of the centers of four outer circles.

Also we know that:

Length of side =2×r=2r

Length of diagonal =r+2R+r=2(R+r)

Therefore, 2(R+r)=2r  

2

​  

 

∴R+r=r  

2

​  

 

Thus, R=r(  

2

​  

−1) is the required inner circle radius r in terms of the outer circles with radius R