The most difficult math Q in the world, “please help if you can”.?

Question

The green circle is the largest of the 3 circles. The red circle is the smallest circle and is located at the centre of the green circle. The yellow circle is the medium sized circle that touches the circumference of the small red circle and touches the circumference of the large green circle. Knowing that both the small red circle and the medium yellow circle are smaller than the large green circle and are placed within the large circle. The centre of the large green circle is O. The smallest circle has centre O and radius 2x centimetres.
The large circle has centre O and radius 2y centimetres. The third circle touches both the other two circles s shown. The three regions formed are coloured red, yellow and green as shown.

Q1) Explain fully why the radius of the third circle is (x + y) centimetres.

Write down, in terms of ㅠ, x and y, expressions for the area of the region that is coloured Q2) yellow,
Q3) green.

The area of the green region is twice the area of the yellow region.
Q4) Use this information to write down an equation involving x and y, and show that it simplifies to y^2 – 6xy + 5x^2 = 0.

Q5) Calculate the fraction of the design that is coloured yellow.

Answer 1

3rd circles diameter = 2x + 2y

Radius = diameter / 2

Radius = x + y

Okay, it touches the circle of both of them, so then the diameter would be the length covered.

The smallest circle and largest circles have the same centers so then it goes from end of radius of smallest to the end of radius of largest. You can draw it out and tell.

Q2) I don't understand what you meant by regions so you'll have to further explain. I'll just say that it is the area of the middle size circle.

Area = pi(x+y)^2

Q3) Area = pi(2y)^2

Q4) pi(2y)^2 = 2(pi(x+y)^2)

4piy^2 = 2pi(x^2 + 2xy + y^2)

2piy^2 = pi(x^2 + 2xy + y^2)

2y^2 = x^2 + 2xy + y^2

x^2 + 2xy - y^2 = 0

(Are you sure that it simplifies to y^2 - 6xy + 5x^2 = 0?)

Q5) Explain more about this so I can understand. What regions are colored yellow?

Answer 2

Q1. The diameter of the yellow circle =2x+2y.
Q2. Yellow region = pi*(x+y)^2 - pi*(2x)^2
Q3. Green region= pi*2y-[yellow region]
Q4. I don't get that equation. From above, pi*2^y-[yellow region]=2*[yellow region] or
pi*2^y= 3*[yellow region]

Answer 3

i bet ur gonna copy our answers lol

Answer 4

math sucks.