2017 · Q91
In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle ?
Elementary MathematicsCircles
- AD(√(2)-1)
- BD(√(2)+1)
- CD(√(2)+2)
- DD(2-√(2))
Explanation
The four D-diameter circles have centers at the corners of a square of side D. The shaded circle's center is the square's center, at distance D√2/2 from each circle's center. Tangency gives D√2/2 = D/2 + r, so r = D(√2−1)/2 and the shaded diameter is D(√2−1): option A.