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)]	\(arctan \left( 2 \right)\)	Numeric : 1.11 Input : 63.43° or 1.11 rad according Angle Unit selected
AngleBisector[(0,1),(0,0),(1,0)]	\(y = x\)	Numeric : \(y = x\) Input : \(- 0.71 x +0.71 y = 0\)
Circumference[x^2+y2=1/sqrt(π)]	\(2 \; \sqrt{\pi \; \sqrt{\pi}}\)	4.72
Distance[(0,0), x + y = 1] Simplify[Distance[(0,0), x+y=1]]	\( \frac{1}\{\sqrt{2}}\) \(\frac{\sqrt{2}}\{2}\)	0.71
Distance[(0,0),x+2y=4] Simplify[Distance[(0,0),x+2y=4]]	\(\frac{4}\{\sqrt{5}}\) \(4 \cdot \frac{\sqrt{5}}\{5}\)	1.79
Distance[(0,4),y=x^2] Simplify[Distance[(0,4),y=x^2]]	\(\sqrt{ \left( \frac{7}\{2} - 4 \right)^\{2} + \left( -\frac{1}\{2} \; \sqrt{14} \right)^\{2}}\) \(\frac{\sqrt{15}}\{2}\)	1.94
Distance[(0.5,0.5),x^2+y2=1] Simplify[ Distance[(0.5,0.5),x^2+y2=1]]	\(\frac{\frac{1}\{\sqrt{2}}}\{\sqrt{2}} \; \sqrt{ \left( -\sqrt{2} + 1 \right) \; \left( -\sqrt{2} + 1 \right) \; \sqrt{2} \; \sqrt{2}}\) \(\frac{-\sqrt{2} + 2}\{2}\)	0.29
Ellipse[(2,1),(5,2),(5,1)]	\(28 \; x^\{2} - 24 \; x \; y - 160 \; x + 60 \; y^\{2} - 96 \; y + 256 = 0\)	Numeric : \(28 \; x^\{2} - 24 \; x \; y - 160 \; x + 60 \; y^\{2} - 96 \; y + 256 = 0\) Input : \(7 \; x^\{2} - 6 \; x \; y + 15 \; y^\{2} - 40 \; x + - 24 \; y = - 64\)
Ellipse[(2,1),(5,2),(6,1)]	\(32 \; x^\{2} \; \sqrt{2} + 36 \; x^\{2} - 224 \; x \; \sqrt{2} - 24 \; x \; y - 216 \; x \; ... \) \( \; ... + 32 \; \sqrt{2} \; y^\{2} - 96 \; \sqrt{2} \; y + 256 \; \sqrt{2} + 68 \; y^\{2} - 120 \; y + 196 = 0\)	Numeric : \(81.25 \; x^\{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^\{2} - 255.76 \; y + 558.04 = 0\) Input : \(81.25 \; x^\{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^\{2} - 255.76 \; y = - 558.04 \)
Radius[x^2+y2=1/sqrt(π)]	\(\frac{\sqrt{\pi \; \sqrt{\pi}}}\{\pi}\)	0.75

Command

Evaluate

Numeric or Input, Rounding 2 Decimal Places

Angle[(1,0),(0,0),(1,2)]

\(arctan \left( 2 \right)\)

Numeric : 1.11 Input : 63.43° or 1.11 rad according Angle Unit selected

AngleBisector[(0,1),(0,0),(1,0)]

\(y = x\)

Numeric : \(y = x\) Input : \(- 0.71 x +0.71 y = 0\)

Circumference[x^2+y2=1/sqrt(π)]

\(2 \; \sqrt{\pi \; \sqrt{\pi}}\)

4.72

Distance[(0,0), x + y = 1] Simplify[Distance[(0,0), x+y=1]]

\( \frac{1}\{\sqrt{2}}\) \(\frac{\sqrt{2}}\{2}\)

0.71

Distance[(0,0),x+2y=4] Simplify[Distance[(0,0),x+2y=4]]

\(\frac{4}\{\sqrt{5}}\) \(4 \cdot \frac{\sqrt{5}}\{5}\)

1.79

Distance[(0,4),y=x^2] Simplify[Distance[(0,4),y=x^2]]

\(\sqrt{ \left( \frac{7}\{2} - 4 \right)^\{2} + \left( -\frac{1}\{2} \; \sqrt{14} \right)^\{2}}\) \(\frac{\sqrt{15}}\{2}\)

1.94

Distance[(0.5,0.5),x^2+y2=1] Simplify[ Distance[(0.5,0.5),x^2+y2=1]]

\(\frac{\frac{1}\{\sqrt{2}}}\{\sqrt{2}} \; \sqrt{ \left( -\sqrt{2} + 1 \right) \; \left( -\sqrt{2} + 1 \right) \; \sqrt{2} \; \sqrt{2}}\) \(\frac{-\sqrt{2} + 2}\{2}\)

0.29

Ellipse[(2,1),(5,2),(5,1)]

\(28 \; x^\{2} - 24 \; x \; y - 160 \; x + 60 \; y^\{2} - 96 \; y + 256 = 0\)

Numeric : \(28 \; x^\{2} - 24 \; x \; y - 160 \; x + 60 \; y^\{2} - 96 \; y + 256 = 0\) Input : \(7 \; x^\{2} - 6 \; x \; y + 15 \; y^\{2} - 40 \; x + - 24 \; y = - 64\)

Ellipse[(2,1),(5,2),(6,1)]

\(32 \; x^\{2} \; \sqrt{2} + 36 \; x^\{2} - 224 \; x \; \sqrt{2} - 24 \; x \; y - 216 \; x \; ... \) \( \; ... + 32 \; \sqrt{2} \; y^\{2} - 96 \; \sqrt{2} \; y + 256 \; \sqrt{2} + 68 \; y^\{2} - 120 \; y + 196 = 0\)

Numeric : \(81.25 \; x^\{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^\{2} - 255.76 \; y + 558.04 = 0\) Input : \(81.25 \; x^\{2} - 24 \; x \; y - 532.78 \; x + 113.25 \; y^\{2} - 255.76 \; y = - 558.04 \)

Radius[x^2+y2=1/sqrt(π)]

\(\frac{\sqrt{\pi \; \sqrt{\pi}}}\{\pi}\)

0.75

Symbolic Computations

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

Command

Evaluate

Numeric

Circle[(a,b),r]

(y - b)² + (x - a)² = r²

Distance[(a,b),(c,d)]

\(\sqrt{ \left( b - d \right)^\{2} + \left( a - c \right)^\{2}}\)

\(\sqrt{a^\{2} - 2 \; a \; c + b^\{2} - 2 \; b \; d + c^\{2} + d^\{2}}\)

Distance[(a,b),p x + q y = r]

Line[(a,b),(c,d)]

\(y = \frac{x}\{a - c} \; \left( b - d \right) + \frac{1}\{a - c} \; \left( a \; d - b \; c \right)\)

\(y = \frac{a \; d - b \; c + b \; x - d \; x}\{a - c}\)

Line[(a,b),y=p x+q]

\(y = p x - a p + b\)

\(y = -a p + b + p x\)

MidPoint[(a,b),(c,d)]

\( \left( \frac{a + c}\{2}, \frac{b + d}\{2} \right) \)

\( \left( 0.5 \; a + 0.5 \; c, 0.5 \; b + 0.5 \; d \right) \)

PerpendicularBisector[(a,b),(c,d)]

\(y = \frac{-a + c}\{b - d} \; x + \frac{a^\{2} + b^\{2} - c^\{2} - d^\{2}}\{2 \; b - 2 \; d}\)

\(y = \frac{a^\{2} - 2 \; a \; x + b^\{2} - c^\{2} + 2 \; c \; x - d^\{2}}\{2 \; b - 2 \; d}\)