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# Machining trygonometry

## Radius from 2 points on a curve

## Find the depth of a sphere section given the radius of the
Sphere (R) and the radius of of the section (a)

If we have a spherical dish - and lay a straight line across the
diameter - the depth (h) can be found.

Where **R** is the Radius of the sphere,

and **a** is the radius of the section(dish),

we find **d** - the depth of the section.

## Radius to 45 Chamfer

## Depth of counter sinks

\begin{align*}

A^2 + B^2 = C^2\\

y^2+B^2=r^2\\

r=B+x\\

y^2+B^2=(B+x)^2\\

y^2+B^2=B^2+2Bx+x^2\\

y^2-x^2=2Bx+x^2\\

B=\frac{y^2-x^2}{2x}\\

r=\frac{y^2-x^2}{2x}+x\\

r=\frac{y^2-x^2+2x^2}{2x}\\

r=\frac{y^2+x^2}{2x}\\

\end{align*}

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