the area of two congruent circle of radius r in cm^2is
Answers
Label the center of the first circle C and the center of the second circle C′. Label one of the points of intersection of the two circles A and the other B. Let the radius of the circles be r>0. It should be clear that the following lengths are all equal to r. AC, AC′, BC, BC′, CC′. With a simple application of Pythagoras' Theorem, we get that the length of the line segment AB is 3–√r.
With some basic trigonometry, we find the angles ∠ACB=∠AC′B=2π3. So, the area of one half of the intersection is the area of a circular segment with angle θ=2π3 and radius r, which gives an area of r22(θ−sinθ)=r22(2π3−3–√2) and so the area of the entire intersection is twice this. This gives an area of
r2(2π3−3–√2).
Answer:
Step-by-step explanation:
Area of circle of radius r = Area of the square of side a
=> πr² = a²
=> r²/a² = 1/π
=> r/a = 1/√π
Thus the ratio of r to a is 1 : √π
Is the required answer.