1. Square in a Circle Start with a square and draw a circle around it.
Divide the square in half on the diagonal
If the side of the square is 5, what is the diagonal
A2 + B2 = C2
= C2
= C2
√ = √C2 = C
√2 x √25 = C
√2 x 5 = 5√2 = C
What’s the green shaded area?
AC = πr2
As = s2
Cc = πD = 2πr
5√ 2 5

2. Square in a circle Ac= π25/2 AC = πr2 As = s2 Cc = πD = 2πr
What’s the green shaded area?
First of all the green shaded area is the area of the circle minus the area of the square.
Area of the square is 5 x 5= 25
Area of the circle is πr2
r = ½ 5√2 = π(5/2√2)2
What !! Don’t panic
5/2 x 5/2 x √2 x √2= 25/4 x 2 =
50/4 = 25/2
Ac= π25/2
Green area= π25/2- 25
Green area= 25(π/2- 1)
AC = πr2
As = s2
Cc = πD = 2πr 5
5√ 2

3. Square in a Circle Area of circle – Area of Square π r2 - s2
If the diagonal = 10 (r = 5)
Shade = 25π - 5√2 x 5√2
Shade = 25π - 50
Shade = 25(π–2)
If the side = 10
Shade = π(5√2 x 5√2) – 10 x 10
Shade = 50π
Shade = 50(π-2) .

4. Circle in a Square . 100 - 25π = 25(4= π) Don’t be fooled
Area of square- Area of circle
s = πr2
If the side =10, radius = 5 (1/2D)
10 x π 52
π = 25(4= π)
Don’t be fooled .

5. Brain teasers