anonymous
  • anonymous
does this diagram provides sufficient information to find the ratio of O1-P to O1-O2 ?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
given 3 circles, the circumference of the 2nd circle cuts the centre of circle1 at O1, while the centre of the 3rd circle is formed between the upper intersection of 1st and 2nd circle, with its circumference cuts through centre of 1st circle. radius of 2nd circle is unknown.
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anonymous
  • anonymous
and a str8 line is formed between O1 and O2, with P be the right intersection of 3rd circle with the line.
amistre64
  • amistre64
O1-P to O1-O2 are these distances

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anonymous
  • anonymous
yep
amistre64
  • amistre64
o1 to p i the base of an iso tri with sides of r|dw:1344615311196:dw|
amistre64
  • amistre64
we can define an angle using o1,o2 and oi,1 so that o1,p is findable to me
amistre64
  • amistre64
err ... o1,o3 that is
amistre64
  • amistre64
|dw:1344615460417:dw|
amistre64
  • amistre64
or really P = (2a,0) in this case :)
amistre64
  • amistre64
|dw:1344615575595:dw| im sure we could come up with something
amistre64
  • amistre64
we can determine a general ratio; and when given specifics we can fill them in
anonymous
  • anonymous
so i will need to come out with 3 ratios for O1P < O1O2, O1P = O1O2, and O1P > O1O2?
anonymous
  • anonymous
because radius for circle 2 is not fixed
amistre64
  • amistre64
radius for circle 2 is "fixed"
anonymous
  • anonymous
owh. k i'll try from here. thx =)
amistre64
  • amistre64
i might be reading the post wrong tho
amistre64
  • amistre64
o2 is solid, so do we assume we know the position of o2 relative to the other solid objects?
anonymous
  • anonymous
erm o2 is the centre of 2nd circle. lol i drawed the dot too big i guess.
anonymous
  • anonymous
its an imaginary centre because radius 2 is unknown.
anonymous
  • anonymous
but centre of circle 2 will be placed same level with circle 1
amistre64
  • amistre64
|dw:1344616423539:dw| well, you do have 3 points of contact for the circle2 i believe
amistre64
  • amistre64
|dw:1344616612225:dw|
amistre64
  • amistre64
the half the length from 03 to 0'3 would be known (y) and half the distance from 01 to P can be known (x) y^2 = x*(distance from p/2 to 03)
amistre64
  • amistre64
|dw:1344616835067:dw| y^2 = x*c ; x+c = radius from 01 to 02
amistre64
  • amistre64
or rather r' = x+c
amistre64
  • amistre64
the ratio then is.... 2x : r'
amistre64
  • amistre64
2x : x+c , and since y^2 = xc; c=y^2/x 2x : x + y^2/x 2x : (x^2 + y^2)/x
anonymous
  • anonymous
o i'll try to digest 'em. really thx for spending time with this question. @@
amistre64
  • amistre64
youre welcome, it was fun :)
anonymous
  • anonymous
y^2 = xc is some theorem? o.o

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