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July 20th, 2017, 08:59 PM   #1
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Post Need help to solve this Geometry question !!!

Hello Everyone,

Please help me solving a geometry related problem which I've attached.

I need to find the value of x.

Thanks in Advance.
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July 20th, 2017, 09:36 PM   #2
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As a function of r1, r2 and a?
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July 20th, 2017, 10:22 PM   #3
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As a function of r1, r2 and a?
Yes,

r1, r2 and a are any numbers greater than 0.
I need to find the value of x in terms of r1, r2 and a.

Last edited by skipjack; July 21st, 2017 at 05:27 AM.
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July 21st, 2017, 05:25 AM   #4
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Can you use coordinate geometry? Start by supplying a label (O, A, B, etc.) for each point where lines (or curves) meet in the diagram. It's then fairly easy to obtain an equation that x satisfies, etc.
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July 21st, 2017, 07:59 PM   #5
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Quote:
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Can you use coordinate geometry? Start by supplying a label (O, A, B, etc.) for each point where lines (or curves) meet in the diagram. It's then fairly easy to obtain an equation that x satisfies, etc.
Yeah, if it can be solved using co-ordinates then please do it, actually I can't figure it out how to solve this problem using co-ordinates.

But solving it using geometry/trigo/algebra will be more useful.

Actually I tried using geometry/trigonometry/algebra but got stuck after finding the value of AB (see attached image).
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Last edited by sagar233; July 21st, 2017 at 08:08 PM.
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July 22nd, 2017, 03:41 AM   #6
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AB has equation x - y - a = 0 (the x here isn't the angle in the diagram).
OP = r1 - r2, so P has coordinates ((r1 - r2)cos(x°), (r1 - r2)sin(x°)).
Hence r2 = |(r1 - r2)cos(x°) - (r1 - r2)sin(x°) - a|/√2 = |(r1 - r2)sin(45° - x°) - a/√2|.

Can you proceed from there?
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July 23rd, 2017, 03:27 AM   #7
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Quote:
Originally Posted by skipjack View Post
AB has equation x - y - a = 0 (the x here isn't the angle in the diagram).
OP = r1 - r2, so P has coordinates ((r1 - r2)cos(x°), (r1 - r2)sin(x°)).
Hence r2 = |(r1 - r2)cos(x°) - (r1 - r2)sin(x°) - a|/√2 = |(r1 - r2)sin(45° - x°) - a/√2|.

Can you proceed from there?
Hi skipjack,
Thanks for reply.

From your equation I'm getting value of
x° = 45° - (sin-¹ ( (r2+a/√2) / (r1 - r2) ) )

But this equation is not giving correct answer.

For Example: if r1 = 10, r2 = 2 and a = 5, then answer x° should be ~33.934
but by above equation I'm getting ~1.216
please check it.

Last edited by sagar233; July 23rd, 2017 at 03:29 AM.
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July 23rd, 2017, 05:18 AM   #8
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The expression (r1 - r2)sin(45° - x°) - a/√2 is negative for your values of a, r1, r2 and x $\small\approx$ 33.934,
so use a/√2 - (r1 - r2)sin(45° - x°) for its absolute value.

Your original calculated value of x corresponds to a diagram in which the smaller circle lies on the other side of the line AB.
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July 23rd, 2017, 06:04 AM   #9
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Quote:
Originally Posted by skipjack View Post
The expression (r1 - r2)sin(45° - x°) - a/√2 is negative for your values of a, r1, r2 and x $\small\approx$ 33.934,
so use a/√2 - (r1 - r2)sin(45° - x°) for its absolute value.

Your original calculated value of x corresponds to a diagram in which the smaller circle lies on the other side of the line AB.
Hi skipjack,

Thanks a lot for this solution.
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