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MATH Geniuses -- I need your help!!!

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Bat-mite

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To anyone who is a math whiz -- I need your help.

Please see the illustration. If I know the radius of a circle, and I know the length of the secant AB, and that's all I know, how do I calculate X (the red segment, i.e., the distance from the secant to the circumference)?

I'm not looking for a math lesson, just a simple equation I can use to measure that distance. Thanks!
 

blackbrandt

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I don't see a pic.

However, if the problem I'm thinking of is the same, you use a triangle to solve it. Post a pic and I'll post a solution. #CalcIIperks
 

Bat-mite

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I don't see a pic.

However, if the problem I'm thinking of is the same, you use a triangle to solve it. Post a pic and I'll post a solution. #CalcIIperks
Woops, I forgot the pic. BUT ... in the mean time, I asked someone in the office and we worked it out. And yes, using a triangle.

As it turns out, it's:

radius - sqrt (radius squared - half the secant squared)

My circle's radius is 3.9285. The width of the secant is 0.4375, so:

3.9285 - sqrt (3.9285^2 - 0.21875^2) = 3.9285 - sqrt (15.43311225 - 0.0478515625) = 3.9285 - sqrt 15.3852606875 = 3.9285 - 3.9224049622011238731396889849811 = 0.00609503779887612686031101501889

I really wanted to know if that distance would be less than 1/32", and 1/32 = 0.03125; so yes, it is about 1/5 of 1/32. So I have the info I need.

Thanks anyway!
 
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