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Browse College Triangles and Other Polygons

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Pick's Theorem [2/8/1996]
I was wondering what Pick's theorem is.

Point within a Triangle [05/29/2003]
I have the coordinates of the three corners of a equilateral triangle ABC. How can I decide whether an arbitrary point (X,Y) lies in the plane of the triangle?

Polygon Algorithms [05/10/2001]
Given a polygon as a set of points (X, Y) and a database table with X and Y columns, select all records/points from the table that are inside the polygon or belong to its border.

Proof of Morley's Theorem [08/09/2000]
How can I prove Morley's theorem (if every angle in a triangle is trisected, each pair of trisectors meets in a point, and all three points form the vertices of an equilateral triangle)?

Proving Concurrence Using Vectors [10/17/2005]
How do you prove that angle bisectors are concurrent using vectors? I have proved this using coordinate geometry, but I do not know how to find the point of intersection using vectors.

Rhombus vs. Rhomboid [08/27/2002]
What is the difference between a rhombus and a rhomboid?

Right Triangle Proof [11/19/2004]
In right triangle ABC, let CD be the altitude to the hypotenuse. If r1,r2,r3 are radii of the incircles of triangles ABC, ADC, and BDC, respectively, prove CD = r1 + r2 + r3.

Simson/Wallace Line Proof [11/19/2002]
From a point P on the circumcircle of the triangle ABC perpendiculars are dropped to the sides AB, BC, CA. Prove that the line joining the feet of the perpendiculars bisects the line joining the orthocentre of triangle ABC and point P.

Sum of Angles of Polygon... [9/24/1996]
Assuming the equality of alternate interior angles formed by a transversal cutting a pair of parallel lines, prove...

Symmedian Point [11/18/2002]
Prove that in the plane of any triangle ABC, with G the centroid, La, Lb, and Lc the bisectors of angles A, B, and C, Ga, Gb, and Gc the reflections of line AG about La, BG about Lb, and CG about Lc, the three lines Ga, Gb, Gc meet in the symmedian point.

Three Pieces of a Stick Forming a Triangle [01/22/2007]
If you break a straight stick into three pieces, what is the probability that you can join the pieces end-to-end to form a triangle?

Triangle Centers at Lattice Points [09/03/2002]
Is there a triangle that can be plotted on a rectangular grid so that all of its vertices and all four centers are lattice points? If so, what are the coordinates of the vertices?

Two Questions on Geometric Harmonics [11/24/2005]
Two circles intersect each other at B and C. Their common tangent touches them at P and Q. A circle is drawn through B and C cutting PQ at L and M. Prove that {PQ:LM} is harmonic.

Uniquely Determining a Polygon [02/05/2001]
Is it true that if you know the side order, side lengths, and area of a polygon, as well as whether each of its angles is obtuse or acute, you have uniquely determined it?

Using the Incenter [05/06/2003]
I need to construct a triangle to fit inside a triangle.

Will the Triangle People Meet? [11/09/2007]
Persons A, B, and C stand at the vertices of an equilateral triangle with 10 meter sides. At the same moment all of them start moving at 1 m/sec. A always heads toward B, B towards C, and C towards A. Will they meet? How long will it take?

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