Results 1 to 6 of 6
Thread: Circles

20080416, 16:48 #1
 Join Date
 Feb 2008
 Posts
 5
 Thanks
 0
 Thanked 0 Times in 0 Posts
Circles
The large circle has a diameter of 1m. The lines are at right angles.
What is the diameter of the small circle?
Tyler

20080416, 17:17 #2
 Join Date
 Mar 2002
 Posts
 84,353
 Thanks
 0
 Thanked 29 Times in 29 Posts
Re: Circles
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">32*SQRT(2) meters</span hide>

20080416, 17:34 #3
 Join Date
 Feb 2008
 Posts
 5
 Thanks
 0
 Thanked 0 Times in 0 Posts
Re: Circles
Nice formula. I used pages of Pythagoras and came out at <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">0.1768, 5mm more</span hide> .
Tyler

20080416, 18:07 #4
 Join Date
 Mar 2002
 Posts
 84,353
 Thanks
 0
 Thanked 29 Times in 29 Posts
Re: Circles
Here is the calculation:
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: 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*(21) = r*(22*SQRT(2)+1)
s = r*(32*SQRT(2)
The diameter of the small circle is 2*s = 2*r*(32*SQRT(2)).
Since r =1/2, s = 32*SQRT(2)</span hide>

20080418, 16:17 #5
 Join Date
 Feb 2008
 Posts
 5
 Thanks
 0
 Thanked 0 Times in 0 Posts
Re: Circles
That’s neat.
I did:
AG = SQRT((CG*CG)+(AC*AC))
= 0.7071
AG+radius = 077071 + 0.5 = 1.2071
AF = 1.2071 – 1 = 0.2071
AE = 0.2071 * 0.7071 = 0.1464
AD = 0.2071 * 0.1464 = 0.03033
DF = (AF) – (AD) = 0.2071 – 0.03033 = 0.17677
Answer = 176.8mm

20080418, 16:28 #6
 Join Date
 Mar 2002
 Posts
 84,353
 Thanks
 0
 Thanked 29 Times in 29 Posts
Re: Circles
I can follow your calculation up to and including the line
AF = 1.2071 – 1 = 0.2071
But I don't understand the next two lines:
AE = 0.2071 * 0.7071 = 0.1464
AD = 0.2071 * 0.1464 = 0.03033