Circs

The large circle is divided into four parts. The two small circles are half the radius of the large one, so have 1/4 the area each. The remaining 2 regions are identical, and together make up the other half of the total area, so must also be 1/4 each.

Let $y$ be the area of yellow/red circle, $b$ be the area of the blue region and $o$ be the area of the orange region.

Let $r$ be the radius of the yellow/red circle, then the radius of the big circle is $2r$ .

So, we have

$y=\pi r^2$

$b=o=\dfrac{\pi (2r)^2-2\pi r^2}{2}=\dfrac{4\pi r^2-2\pi r^2}{2}=\dfrac{2\pi r^2}{2}=\pi r^2$

$\color{#D61F06} \large{\therefore}$ $\boxed{\color{plum}\text{The four areas are equal.}}$

I don't get all of you guys, nor this question. What's with the complicated thinking process? The question says that they're identical, so what's there to calculate?

Let radius of small circle be r So radius of big circle is 2r Area of yellow circle is (pi)r^2 and area of both smaller circles is 2 (pi)r^2 Now Area of big circle is 4 (pi)r^2 Hence area of blue and orange region together is also 2(pi)r^2 and as they are similar each blue / orange region area is (pi)r^2 So blue. yellow, red, orange all have same area

The are formula for a circle is $πr^2$ . The definition of the radius (r) is $\frac{d}{2}$ , with $d$ being the diameter. Therefore, if the two circles have an equal diameter, they must also have an equal area, as the diameter/radius of a circle is what defines the area.

You can solve it by looking at the options:-

It can't be blue as blue will be equal to orange.

It can't be yellow as yellow will be equal to red.

So answer is option 3 which is all are equal.

The diameter of one of the smaller circles is the radius of the big one, which can be applied horizontally and also vertically wich means that the area of the big circle is sum of 4 smaller circles. Or: 1small circle is 1/4 of the big one.

The two smaller circles have a radius half than radius of big circle.Then the areas of small circles are 1/4 of the large one. Considering - Area(big circle)=1 - Area(red circle) + area(yellow circle) =1/2 then area(blue) = 1/4 = area(green region) also area(red circle)= area(yellow circle)=1/4

Pi rsqu - 2(pi (r/2)squ)=pi rsqu-2pi(dsqu/4) =pi rsqu-2pirsqu/4=(4pi*rsqu)/4-2pirsqu/4 =2pirsqu/4 so the sum of the area of the small circles equals the remainder of the large cicle. Did u get that?

since the yellow (Y) section = red (R) section and they both add up to the diameter of the total, so area of of Yellow is (pi*(1/2r)^2) = pi * 1/4 of r^2 so area of Y is a 1/4 of the whole circle (yellow + blue + red + orange). Now we can see that the blue (B) section is equal to half the area of the whole circle - the half the area of Y and R (which is equal) so it can be written as: AreaB = 1/2(AreaWholeCircle) - AreaY. so so it is half - quartre of the whole circle = 1/4. so it is equal to Y

Both the circles (inside )are same in area and they are on diameter of outer circle. So the amount of loss of area in both regions is same...(it will have different areas when both inner circles are not in same line )

Let d be the diameter of the large circle. The area of a circle, expressed in terms of diameter, is $A_{circle} = \pi(\frac{d}{2})^2 = \frac{\pi}{4}d^2$ . The area of a smaller circle with diameter $\frac{d}{2}$ is $A_y = \frac{\pi}{4}(\frac{d}{2})^2 = \frac{\pi}{16}d^2$ . The area of both circles is twice the area of one of them is $A_{r+y} = \frac{\pi}{8}d^2$ . The rest of the circle's area is the area of the circle minus the area of the two circles is $A_{b+o} = \frac{\pi}{4}d^2 - \frac{\pi}{8}d^2 = \frac{\pi}{8}d^2$ . Regions b and o are identical, so we can divide that area by two to get $A_b = \frac{\pi}{16}d^2 = A_y$ . The blue and yellow regions have the same area.

It states the two circles are identical. So obviously they have the same area. This is like the old question "which is heavier a pound of lead or a pound of feathers?"