Question

In this diagram,
three concentric circles
rectangle. Point C lies on the middle
have their centers at O, and OABC is a
lies on the outer circle.
circle, point A lies on the inner circle, and point B
the smallest circle.
The intersection point of the rectangle's diagonals also lies on
1. If the radius of the smallest circle is 3, find its area.
2. Find the area of the yellow ring.
3. Find the area of the white ring.
I just need help on 2&3 i dont really know how to do that!

Answer 1

The area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

What is the area of the circle?

The area of the circle is the space occupied by it. It can be given as,

$A=\pi r^2$

Here (r) is the radius of the circle.

In this diagram, three concentric circles' rectangle.

• Point C lies in the middle have their centers at O, and OABC is a lies on the outer circle.
• Point A lies on the inner circle, and point B the smallest circle.

• 1. The area of the smallest circle-

The radius of the smallest circle is 3.

$r_1=3\rm\unit$

Thus, the area of it is,

$A=\pi (3)^2\\A=28.27\rm\; unit^2$

• 2. The area of the yellow ring.

Let suppose the mid-point of the rectangle is D. Here, OB is the diagonal of the rectangle in which,

$OD=BD$  

The radius of the yellow ring's outer face from point O is,

$r_3=OD+BD\\r_3=OD+OD\\r_3=2OD$

OD is the radius of the small circle, which is 3 units long. Thus,

$r_3=2\times3\\r_3=6\rm\; units$

The line segment OC is the radius of the white circle from point O. In the triangle COB from the Pythagoras theorem, the radius r₂ of the middle circle is,

$r_2=\sqrt{r_3^2-r_1^2}\\r_2=\sqrt{6^2-3^2}\\r_2=3\sqrt3$

Thus, the area of the yellow ring is,

$A_y=\pi r_3^2-\pi r_2^2\\A_y=\pi (6)^2-\pi (3\sqrt{3})^2\\A_y=28.27\rm\; unit^2$

• 3. The area of the white ring.

The area of white ring is,

$A_w=\pi r_2^2-\pi r_1^2\\A_w=\pi (3\sqrt{3})^2-\pi (3)^2\\A_w=56.55\rm\; unit^2$

Hence, the area of the smallest circle with radius 3 is 28.27 unit². The area of the yellow ring and white ring is 28.27 unit² and 56.55 unit².

Learn more about the area of the circle here;

https://brainly.com/question/402655

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