Find the area of this circle?
Answers
Given : A circle , & 4 Squares inside Circle
To find : Area of circle
Solution:
We have to see things very carefully
Each Square has area 16
=> Side of each square = 4
Now Horizontal Distance between left side of left most Square & right side of right most Square
= 4 + 4 + 4 + 4 = 16
Right side of right most square is a Chord
Perpendicular bisector of Chord Meets at center of Circle
Let say x is the horizontal Distance of center from right side ( chord) of right most Square
So we will have
radius² = x² + (4/2)²'
=> r² = x² + 4
Now seeing from bottom left vertex of left most square
Horizontal Distance of center would be = 16 - x
& vertical Distance of center would be = 4 + 4/2 = 6
again
r² = (16- x)² + 6²
=> r² = x² + 292 - 32x
Equating r²
=> x² + 4 = x² + 292 - 32x
=> 32x = 288
=> x = 9
r² = x² + 4
=> r² = 9² + 4
=> r² = 85
Area of circle = π r² = 85π sq units
Area of circle = 85π sq units ≈ 267 sq units
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