# Mathematical Experiment 9

The basic commands contained in the packge Geometry are draw and detail.

To create geometric objects, use the following function calls:

circle, conic, dsegment, ellipse, hyperbola, line, parabola, point, segment, square, triangle.

1. Draw the triangle with vertices located at the points A(1,2),B(1,3),C(2,4) together with its circumcircle.
2. Draw the circle given by the equation
3.  x2-2x+2+y2+4y = 0.
4. Draw the parabola given by the equation
5.  y2+12x-6y+33 = 0.
6. Draw the conic passing through points (1,2),(2,3),(-1,2),(0,2),(1,1).
The following functions relating to a triangle are supported:
1. Points of interest: GergonnePoint, NagelPoint, centroid, orthocenter.
2. Lines of interest: EulerLine, ExternalBisector, SimsonLine, altitude, bisector, median.
3. Circles of interest: EulerCircle, circumcircle, excircle, incircle
4. Others: AreConjugate, AreSimilar, IsEquilateral, IsRightTriangle, PedalTriangle, area, medial, method, sides
Commands related to the circle:

• Given three disjoint circles, draw all possible Appolonius circles.
Construct this with Maple:
• Draw the same picture with Geometer's Sketchpad.
• Construct the inversion of a point with respect to a circle
• Construct the inversion of a circle with respect to another given circle.
• Construct an ellipse.
• Construct a hyperbola.
• Construct a parabola.
• Construct the inversion of an ellipse with respect to a given circle.
• Construct the inversion of a hyperbola with respect to a given circle.
• Construct the inversion of a parabola with respect to a given circle.

exp9.tex