# Geometry poblem

Discussion in 'Engineers' Talk' started by candoabitofmoststuff, Jul 18, 2022.

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1. ### candoabitofmoststuffScrewfix Select

Folks,
despite being a whizz at maths when I was at school, getting both O and A levels, and geometry being my strong point then... it was nearly 50 years ago and I cant remember how to do this...

I need to make a couple of circular templates out of card for a small woodwork project...

I know this should be quite straightforward, and If I could work out how to use LibreCad I'd do it on that... However, I can't, so...

Can any kind soul calculate for me what is the radius of a circle that passes through points A,B and C in this diagram with the included measurements.... and also what would the radius be if the long dimension, (256), was only 98? (The "height" would stay the same at 28)
I should have marked it before scanning, but the line from point B meets AC at 90 degrees.

Thanks in advance,
Regards,
Cando

2. ### NotnowvicarActive Member

So you want the line AB which is the same as BC so its pythag...A** + B** = C** where ** is the square. So times the distance A to O by itself( O is the origin the bit where the line from B joins the line AC) and then add the OB length times itself and then square root that answer.

128*128 = 16384 + 28*28 =784 = 17168 and to find the length AB you just square route 17168 = 131.026714833 or 131mm in good enough measurement.

3. ### stevie22Screwfix Select

Wrong Notnow. It's 306.5714,

Being older and wiser than when I learned that stuff I just used AutoCAD

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4. ### WillyEckerslikeScrewfix Select

Different problem - same solution

https://community.screwfix.com/threads/p-shaped-bath-screen.251496/#post-2008402

Edit: For those that cannot be bothered to look (it is very hot after all) the required formula is radius R=((L/2)²+H²))/2H where L is the length of the chord and H is the perpendicular height

As stated above, the answer is 306.5714 using the formula

Edit 2: For a chord of 98mm the radius would be 56.875mm

Last edited: Jul 18, 2022
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5. ### chesterwWell-Known Member

Line B must extend down 100mm to the "centre" of circle. Therefore ratio of radii equals 100 divide by 28 = 3.57 x A128 = 457

6. ### candoabitofmoststuffScrewfix Select

Thanks Notnow... That give me AB, which I could do, as you say simple pythagoras... I want the radius of circle that passes through points A,B and C

7. ### candoabitofmoststuffScrewfix Select

Thank you Stevie... And at the risk of being pushy, I'll take that as correct, (though your .pdf didn't really help!), could you oblige me by giving radius of AC is 98?

Many thanks,
Cando

9. ### candoabitofmoststuffScrewfix Select

Thanks Willy!
Cando

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10. ### FlyByNightScrewfix Select

Going back to first principles:

Radius = r
height of segment = h
chord length = 2l

Half chord makes a right angle triangle when point on circumference is connected back to teh centre.

r^2 = l^2 +(r-h)^2

expanding gives r^2 = l^2 + r^2 - 2rh + h^2

removing r^2 from each side: 0=l^2-2rh + h^2

and then: 2rh = l^2 + h^2

divide both sides by 2h: r = (l^2 + h^2)/2h

insert values: r = (128^2 + 28^2)/2+28

r = (16384 + 784) / 56

r= 17168 / 56

r = 306.5714285

11. ### candoabitofmoststuffScrewfix Select

Thanks again all...
When I tried it it all looked wrong... I'm blaming the heat, but I had my initial measurements wrong... Anyway, with your help I had the formula so was able to find the correct answers I needed.
All done now!

I knew I'd get the solution here!
Cando

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