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Browse College Triangles and Other Polygons
Stars indicate particularly interesting answers or
good places to begin browsing.
 Overlapping right triangle problem [09/14/1997]

Given right triangles ABC and DCB with rt angles at B and C, triangle
ABC's hypotenuse 20 and triangle DCB's hypotenuse 30. The hypotenuses
intersect at point E, a distance of 10 from BC. Find the length of BC.
 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 endtoend 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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