1. ## Circles

The large circle has a diameter of 1m. The lines are at right angles.

What is the diameter of the small circle?

Tyler

2. ## Re: Circles

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3-2*SQRT(2) meters</span hide>

3. ## Re: Circles

Nice formula. I used pages of Pythagoras and came out at <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">0.1768, 5mm more</span hide> .

Tyler

4. ## Re: Circles

Here is the calculation:

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Let's call the radius of the large circle r and that of the small circle s
BD = BC = r.
Angle CAB is 45 degrees, so AB = BC/SQRT(2) = r/SQRT(2)
PS = PC = s
Angle CPQ is 45 degrees, so PQ = PC/SQRT(2) = s/SQRT(2)
r = BD = AB + DA = AB + SQ = AB + SP + PQ = r/SQRT(2) + s + s/SQRT(2)
Multiply both sides of the equation with SQRT(2):
r*SQRT(2) = r + s*SQRT(2) + s
s*(SQRT(2)+1) = r*(SQRT(2)-1)
Multiply both sides with SQRT(2)-1:
s*(SQRT(2)+1)*(SQRT(2)-1) = r*(SQRT(2)-1)*(SQRT(2)-1)
s*(2-1) = r*(2-2*SQRT(2)+1)
s = r*(3-2*SQRT(2)
The diameter of the small circle is 2*s = 2*r*(3-2*SQRT(2)).
Since r =1/2, s = 3-2*SQRT(2)</span hide>

5. ## Re: Circles

That’s neat.

I did:

A-G = SQRT((C-G*C-G)+(A-C*A-C))
= 0.7071

A-G+radius = 077071 + 0.5 = 1.2071

A-F = 1.2071 – 1 = 0.2071

A-E = 0.2071 * 0.7071 = 0.1464

A-D = 0.2071 * 0.1464 = 0.03033

D-F = (A-F) – (A-D) = 0.2071 – 0.03033 = 0.17677

6. ## Re: Circles

A-F = 1.2071 – 1 = 0.2071

But I don't understand the next two lines:

A-E = 0.2071 * 0.7071 = 0.1464

A-D = 0.2071 * 0.1464 = 0.03033

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