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

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- anonymous

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

- chestercat

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- 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.

##### 1 Attachment

- anonymous

and a str8 line is formed between O1 and O2, with P be the right intersection of 3rd circle with the line.

- amistre64

O1-P to O1-O2 are these distances

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- anonymous

yep

- amistre64

o1 to p i the base of an iso tri with sides of r|dw:1344615311196:dw|

- amistre64

we can define an angle using o1,o2 and oi,1 so that o1,p is findable to me

- amistre64

err ... o1,o3 that is

- amistre64

|dw:1344615460417:dw|

- amistre64

or really P = (2a,0) in this case :)

- amistre64

|dw:1344615575595:dw|
im sure we could come up with something

- amistre64

we can determine a general ratio; and when given specifics we can fill them in

- anonymous

so i will need to come out with 3 ratios for O1P < O1O2, O1P = O1O2, and O1P > O1O2?

- anonymous

because radius for circle 2 is not fixed

- amistre64

radius for circle 2 is "fixed"

- anonymous

owh. k i'll try from here. thx =)

- amistre64

i might be reading the post wrong tho

- amistre64

o2 is solid, so do we assume we know the position of o2 relative to the other solid objects?

- anonymous

erm o2 is the centre of 2nd circle. lol i drawed the dot too big i guess.

- anonymous

its an imaginary centre because radius 2 is unknown.

- anonymous

but centre of circle 2 will be placed same level with circle 1

- amistre64

|dw:1344616423539:dw|
well, you do have 3 points of contact for the circle2 i believe

- amistre64

|dw:1344616612225:dw|

- 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

|dw:1344616835067:dw|
y^2 = x*c ; x+c = radius from 01 to 02

- amistre64

or rather r' = x+c

- amistre64

the ratio then is.... 2x : r'

- 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

o i'll try to digest 'em. really thx for spending time with this question. @@

- amistre64

youre welcome, it was fun :)

- anonymous

y^2 = xc is some theorem? o.o

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