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geometry

 FindAngle
 find the angle between two lines or two circles

 Calling Sequence FindAngle(u, v)

Parameters

 u, v - two lines or circles

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{_EnvHorizontalName}≔'x':$$\mathrm{_EnvVerticalName}≔'y':$
 > $\mathrm{line}\left(\mathrm{l1},x+y=1\right),\mathrm{line}\left(\mathrm{l2},x-y=1\right)$
 ${\mathrm{l1}}{,}{\mathrm{l2}}$ (1)
 > $\mathrm{circle}\left(\mathrm{c1},{x}^{2}+{y}^{2}=1\right),\mathrm{circle}\left(\mathrm{c2},{\left(x-2\right)}^{2}+{y}^{2}=4\right)$
 ${\mathrm{c1}}{,}{\mathrm{c2}}$ (2)
 > $\mathrm{FindAngle}\left(\mathrm{l1},\mathrm{l2}\right)$
 $\frac{{1}}{{2}}{}{\mathrm{π}}$ (3)
 > $\mathrm{FindAngle}\left(\mathrm{c1},\mathrm{c2}\right)$
 ${\mathrm{arccos}}{}\left(\frac{{1}}{{8}}{}\sqrt{{4}}\right)$ (4)