# Geometry Formulas for Finding the Radius

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Geometry formulas for finding the radius will often format the element you're looking for as X. Find out about geometry formulas for finding the radius with help from an experienced mathematics educator in this free video clip.

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## Video Transcript

Hello, my name is Walter Unglaub, and this is geometry formulas for finding the radius. If I have a circle in the X, Y plane and I want to solve for the radius, I have to be given some information. I can consider the relationship between the X component of this radial vector going from the center of the circle, the origin and the point on the circle and that relationship is given for X as X equals the radius times cosine of the angle theta that is made between this vector and the X axis and likewise I have Y is equal to R times sine of theta. So if I know the value of X and Y at this coordinate point then I can solve for theta and it's going to be equal to the arc tangent of Y/X which represents the slope on this line and I can use either of these equations to solve for the radius. So using the top equation I have R is equal to my value of X divided by cosine theta where for theta I would plug in this expression because I know my Y and I know my X. Alternatively, we can look at the equation for the circle in standard form which is given by X minus X not squared plus Y minus Y not squared is equal to the radius squared. When I solve this equation of the circle for R I'm interested only in positive values so I have R is equal to positive square root of X minus X not squared plus Y minus Y not squared. In this case, for this example, the center of the circle is located at the origin. So my X not and my Y not are 0 and 0 respectively. So this equation simplifies to R is equal to the square root of X squared plus Y squared which merely represents an application of the Pythagorean Theorem for this little triangle right here. So if I know my X and my Y value along the circle, then I can calculate the radius R. My name is Walter Unglaub, and this is geometry formulas for finding the radius.

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