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edr1c

  • 2 years ago

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

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  1. edr1c
    • 2 years ago
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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.

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  2. edr1c
    • 2 years ago
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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.

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

  4. edr1c
    • 2 years ago
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    yep

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  23. amistre64
    • 2 years ago
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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)

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

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

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

  27. amistre64
    • 2 years ago
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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

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

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

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

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