D is the diameter of each circle. What is the diameter of the shaded circle
In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle?
- D(√2 - 1)
- D(√2 + 1)
- D(√2 + 2)
- D(2 - √2)
Answer
Draw a square joining the centres of the four circle.
The side of such a square = D
Diagonal of the square = √2D
Now, the diagonal of the square is equal to the sum of diameter of bigger circle and diameter of shaded circle.
√2D = D + d
d = D(√2 - 1)
The correct option is A.