The routine finds the angle between two lines u and v, or between two circles u and v.

When u and v are two lines, the smaller angle between two lines is reported.

When u and v are two circles, the angle returned is in the range 0..Pi.

The command with(geometry,FindAngle) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{\_EnvHorizontalName}≔'x'\:$$\mathrm{\_EnvVerticalName}≔'y'\:$

$\mathrm{line}\left(\mathrm{l1}\,x+y=1\right),\mathrm{line}\left(\mathrm{l2}\,x-y=1\right)$

$\mathrm{l1},\mathrm{l2}$

$\mathrm{circle}\left(\mathrm{c1}\,x^2+y^2=1\right),\mathrm{circle}\left(\mathrm{c2}\,{\left(x-2\right)}^2+y^2=4\right)$

$\mathrm{c1},\mathrm{c2}$

$\mathrm{FindAngle}\left(\mathrm{l1}\,\mathrm{l2}\right)$

$\frac{\mathrm{\pi }}{2}$

$\mathrm{FindAngle}\left(\mathrm{c1}\,\mathrm{c2}\right)$

$\arccos \left(\frac{\sqrt{4}}{8}\right)$