ABCD is a square with side length R. Find the radius of the red circle in terms of R?

(R - d)^2 = R^2 - (R/2)^2
(R - d) =√(3/4)*R
d = R(1 - (√3/2))
Radius of small circle = (R/2)(1 - (√3/2)).

answer Aug 24, 2019 by Tejas Naik

Similar Puzzles

0 votes

Square ABCD has a side length of 4. Construct a quarter circle with radius 4 centered at B and a semi-circle............

Square ABCD has a side length of 4. Construct a quarter circle with radius 4 centered at B and a semi-circle with diameter AD. What is the area of overlap between the quarter circle and semicircle?

0 votes

In a square with a side length of 1, two quarter circles are drawn...........What is the radius of the inscribed circle?

In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram.
What is the radius of the inscribed circle?

0 votes

A square has a side length of 7. On each corner, a quarter circle with radius 3 is constructed with the corner........

A square has a side length of 7. On each corner, a quarter circle with radius 3 is constructed with the corner as its center. And on the midpoint of each side, a semicircle with radius 2 is constructed with the midpoint as its center. What is the difference between the orange shaded areas and the blue shaded areas?