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edr1c Group Title

does this diagram provides sufficient information to find the ratio of O1-P to O1-O2 ?

  • 2 years ago
  • 2 years ago

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  1. edr1c Group Title
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    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.

    • 2 years ago
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  2. edr1c Group Title
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    and a str8 line is formed between O1 and O2, with P be the right intersection of 3rd circle with the line.

    • 2 years ago
  3. amistre64 Group Title
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    O1-P to O1-O2 are these distances

    • 2 years ago
  4. edr1c Group Title
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    yep

    • 2 years ago
  5. amistre64 Group Title
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    o1 to p i the base of an iso tri with sides of r|dw:1344615311196:dw|

    • 2 years ago
  6. amistre64 Group Title
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    we can define an angle using o1,o2 and oi,1 so that o1,p is findable to me

    • 2 years ago
  7. amistre64 Group Title
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    err ... o1,o3 that is

    • 2 years ago
  8. amistre64 Group Title
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    |dw:1344615460417:dw|

    • 2 years ago
  9. amistre64 Group Title
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    or really P = (2a,0) in this case :)

    • 2 years ago
  10. amistre64 Group Title
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    |dw:1344615575595:dw| im sure we could come up with something

    • 2 years ago
  11. amistre64 Group Title
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    we can determine a general ratio; and when given specifics we can fill them in

    • 2 years ago
  12. edr1c Group Title
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    so i will need to come out with 3 ratios for O1P < O1O2, O1P = O1O2, and O1P > O1O2?

    • 2 years ago
  13. edr1c Group Title
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    because radius for circle 2 is not fixed

    • 2 years ago
  14. amistre64 Group Title
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    radius for circle 2 is "fixed"

    • 2 years ago
  15. edr1c Group Title
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    owh. k i'll try from here. thx =)

    • 2 years ago
  16. amistre64 Group Title
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    i might be reading the post wrong tho

    • 2 years ago
  17. amistre64 Group Title
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    o2 is solid, so do we assume we know the position of o2 relative to the other solid objects?

    • 2 years ago
  18. edr1c Group Title
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    erm o2 is the centre of 2nd circle. lol i drawed the dot too big i guess.

    • 2 years ago
  19. edr1c Group Title
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    its an imaginary centre because radius 2 is unknown.

    • 2 years ago
  20. edr1c Group Title
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    but centre of circle 2 will be placed same level with circle 1

    • 2 years ago
  21. amistre64 Group Title
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    |dw:1344616423539:dw| well, you do have 3 points of contact for the circle2 i believe

    • 2 years ago
  22. amistre64 Group Title
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    |dw:1344616612225:dw|

    • 2 years ago
  23. amistre64 Group Title
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    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)

    • 2 years ago
  24. amistre64 Group Title
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    |dw:1344616835067:dw| y^2 = x*c ; x+c = radius from 01 to 02

    • 2 years ago
  25. amistre64 Group Title
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    or rather r' = x+c

    • 2 years ago
  26. amistre64 Group Title
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    the ratio then is.... 2x : r'

    • 2 years ago
  27. amistre64 Group Title
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    2x : x+c , and since y^2 = xc; c=y^2/x 2x : x + y^2/x 2x : (x^2 + y^2)/x

    • 2 years ago
  28. edr1c Group Title
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    o i'll try to digest 'em. really thx for spending time with this question. @@

    • 2 years ago
  29. amistre64 Group Title
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    youre welcome, it was fun :)

    • 2 years ago
  30. edr1c Group Title
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    y^2 = xc is some theorem? o.o

    • 2 years ago
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