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Given four points A, B, C, F, the routine CrossRatio(A, B, C, F) computes the cross ratio of A, B, C, F taken in this order.

If A, B, C, F are four distinct points on an ordinary line, the cross ratio of A, B, C, F taken in this order is defined as:

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

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

$\mathrm{point}\left(A\,0\,0\right),\mathrm{point}\left(B\,3\,3\right),\mathrm{point}\left(C\,7\,7\right),\mathrm{point}\left(F\,\frac{21}{11}\,\frac{21}{11}\right)\:$

$\mathrm{CrossRatio}\left(A\,B\,C\,F\right)$

$-\frac{\sqrt{98}\sqrt{32}\sqrt{882}\sqrt{288}}{28224}$

$\mathrm{CrossRatio}\left(A\,C\,B\,F\right)$

$\frac{\sqrt{18}\sqrt{32}\sqrt{882}\sqrt{6272}}{28224}$