Radius of an Arch
Date: 05/25/98 at 15:52:07 From: Travis Bullard Subject: Radius of circle Is there a simple formula to calculate the radius of a circle where the chord length and a distance from the centre of the chord to the circumference are known? This is for my dad who is a carpenter. He needs it to scribe archways in windows and door openings. Thank you for your attention.
Date: 06/06/98 at 12:52:26 From: Doctor Jeremiah Subject: Re: Radius of circle Hi Travis: There is a fairly simple equation to find the radius: |-------------L-------------| +++++++ --- --- + + | | + + d | + + | | +---------------------------+ --- | R | | | + <=== circle center --- Here is the information we have: L is the Length of the chord length d is the distance from the centre of the chord to the circumference Here is the information we are trying to find: R is the Radius of the circle Let's add a few dimensions to our drawing: The radius (R) of the circle is the distance from the center to any point on the circumference. We also need the length from the end of the chord to halfway along where it crosses the center mark. This is the chord length divided by two. The distance from the center of the circle to the chord is the radius of the circle (R) minus the distance from the chord to the edge. |-----L/2-----| +++++++ + + + + + + +---------------------------+ --- + | + | R R-d + | + --- If we draw it like this where d and L are known then we have a right angle triangle: +++++++ + + + + + + +------L/2----+ ------------+ + | + | R R-d + | + The Pythagorean Theorem can be used: R^2 = (L/2)^2 + (R-d)^2 Now we just have to solve for R. That means we have to expand (R-d)^2 by squaring it. Then we simplify and collect terms. The resulting equation is quite simple. If you need more help write me back. -Doctor Jeremiah, The Math Forum Check out our web site! http://mathforum.org/dr.math
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.