Two triangles T1 and T2 are said to be conjugate, or polar, for a circle c if each vertex of one triangle is the pole of a side of the other triangle.

The routine returns true if T1 and T2 are conjugate for c; false if they are not.

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

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

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

$\mathrm{triangle}\left(\mathrm{T1}\,\left[\mathrm{point}\left(\mathrm{P1}\,1\,\frac{3}{2}\right)\,\mathrm{point}\left(\mathrm{P2}\,2\,1\right)\,\mathrm{point}\left(\mathrm{P3}\,0\,1\right)\right]\right)\:$

$\mathrm{line}\left(\mathrm{l1}\,y=0\,\left[x\,y\right]\right),\mathrm{line}\left(\mathrm{l2}\,y=x\,\left[x\,y\right]\right),\mathrm{line}\left(\mathrm{l3}\,x+y-2=0\,\left[x\,y\right]\right)\:$

$\mathrm{triangle}\left(\mathrm{T2}\,\left[\mathrm{l1}\,\mathrm{l2}\,\mathrm{l3}\right]\right)\:$

$\mathrm{circle}\left(c\,\left[\mathrm{point}\left(o\,1\,2\right)\,1\right]\right)$

$c$

$\mathrm{AreConjugate}\left(\mathrm{T1}\,\mathrm{T2}\,c\right)$

$\mathrm{true}$