# CAS View Supported Geometry Commands

From GeoGebra 5 onwards, the CAS View supports exact versions of the following Geometry Commands.

## Exact Calculations

Command Evaluate Numeric
or Input,
Rounding 2 Decimal Places
Angle[(1,0),(0,0),(1,2)] \mathrm{\mathsf{ arctan \left( 2 \right) }} Numeric : 1.11
Input : 63.43° or 1.11 rad according Angle Unit selected
AngleBisector[(0,1),(0,0),(1,0)] \mathrm{\mathsf{ y = x }} Numeric : \mathrm{\mathsf{ y = x }}
Input : \mathrm{\mathsf{ - 0.71 x +0.71 y = 0 }}
Circumference[x^2+y^2=1/sqrt(π)] \mathrm{\mathsf{ 2 \; \sqrt{\pi \; \sqrt{\pi}} }} 4.72
Distance[(0,0), x + y = 1]

Simplify[Distance[(0,0), x+y=1]]
\mathrm{\mathsf{ \frac{1}{\sqrt{2}} }}

\mathrm{\mathsf{ \frac{\sqrt{2}}{2} }}
0.71
Distance[(0,0),x+2y=4]

Simplify[Distance[(0,0),x+2y=4]]
\mathrm{\mathsf{ \frac{4}{\sqrt{5}} }}

\mathrm{\mathsf{ 4 \cdot \frac{\sqrt{5}}{5} }}
1.79
Distance[(0,4),y=x^2]

Simplify[Distance[(0,4),y=x^2]]
\mathrm{\mathsf{ \sqrt{ \left( \frac{7}{2} - 4 \right)^{2} + \left( -\frac{1}{2} \; \sqrt{14} \right)^{2}} }}

\mathrm{\mathsf{ \frac{\sqrt{15}}{2} }}
1.94

Distance[(0.5,0.5),x^2+y^2=1]

Simplify[ Distance[(0.5,0.5),x^2+y^2=1]]
\mathrm{\mathsf{ \frac{\frac{1}{\sqrt{2}}}{\sqrt{2}} \; \sqrt{ \left( -\sqrt{2} + 1 \right) \; \left( -\sqrt{2} + 1 \right) \; \sqrt{2} \; \sqrt{2}} }}

\mathrm{\mathsf{ \frac{-\sqrt{2} + 2}{2} }}
0.29
Ellipse[(2,1),(5,2),(5,1)] \mathrm{\mathsf{ 28 \; x^{2} - 24 \; x \; y - 160 \; x + 60 \; y^{2} - 96 \; y + 256 = 0 }} Numeric : \mathrm{\mathsf{ 28 \; x^{2} - 24 \; x \; y - 160 \; x + 60 \; y^{2} - 96 \; y + 256 = 0 }}
Input : \mathrm{\mathsf{ 7 \; x^{2} - 6 \; x \; y + 15 \; y^{2} - 40 \; x + - 24 \; y = - 64 }}
Ellipse[(2,1),(5,2),(6,1)] \mathrm{\mathsf{ 32 \; x^{2} \; \sqrt{2} + 36 \; x^{2} - 224 \; x \; \sqrt{2} - 24 \; x \; y - 216 \; x \; ... }}
\mathrm{\mathsf{ \; ... + 32 \; \sqrt{2} \; y^{2} - 96 \; \sqrt{2} \; y + 256 \; \sqrt{2} + 68 \; y^{2} - 120 \; y + 196 = 0 }}
Numeric : \mathrm{\mathsf{ 81.25 \; x^{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^{2} - 255.76 \; y + 558.04 = 0 }}
Input : \mathrm{\mathsf{ 81.25 \; x^{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^{2} - 255.76 \; y = - 558.04 }}
Radius[x^2+y^2=1/sqrt(π)] \mathrm{\mathsf{ \frac{\sqrt{\pi \; \sqrt{\pi}}}{\pi} }} 0.75

## Symbolic Computations

Command Evaluate Numeric
Circle[(a,b),r] (y - b)² + (x - a)² = r²
Distance[(a,b),(c,d)] \mathrm{\mathsf{ \sqrt{ \left( b - d \right)^{2} + \left( a - c \right)^{2}} }} \mathrm{\mathsf{ \sqrt{a^{2} - 2 \; a \; c + b^{2} - 2 \; b \; d + c^{2} + d^{2}} }}
Distance[(a,b),p x + q y = r]
Line[(a,b),(c,d)] \mathrm{\mathsf{ y = \frac{x}{a - c} \; \left( b - d \right) + \frac{1}{a - c} \; \left( a \; d - b \; c \right) }} \mathrm{\mathsf{ y = \frac{a \; d - b \; c + b \; x - d \; x}{a - c} }}
Line[(a,b),y=p x+q] \mathrm{\mathsf{ y = p x - a p + b }} \mathrm{\mathsf{ y = -a p + b + p x }}
MidPoint[(a,b),(c,d)] \mathrm{\mathsf{ \left( \frac{a + c}{2}, \frac{b + d}{2} \right) }} \mathrm{\mathsf{ \left( 0.5 \; a + 0.5 \; c, 0.5 \; b + 0.5 \; d \right) }}
PerpendicularBisector[(a,b),(c,d)] \mathrm{\mathsf{ y = \frac{-a + c}{b - d} \; x + \frac{a^{2} + b^{2} - c^{2} - d^{2}}{2 \; b - 2 \; d} }} \mathrm{\mathsf{ y = \frac{a^{2} - 2 \; a \; x + b^{2} - c^{2} + 2 \; c \; x - d^{2}}{2 \; b - 2 \; d} }}
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