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Outline
Geometrium
A new generalization of Bottema's theorem
Area of a rhombus
Area of a regular convex pentagon
A conic inside a hexagon
An ellipse inside a heptagon
Intersecting circles
Concurrent point in an arbitrary triangle
A generalization of Droz-Farny line theorem
Equal sums of triangle areas
A generalization of Thébault's theorem
A rhombus inside a parallelogram
Square inside a square
Equilateral triangle inside an equilateral triangle
A concyclic points inside a pentagon
Point of concurrency in an arbitrary triangle
Point of concurrency in a cyclic pentagon
Point of concurrency in a cyclic quadrilateral
Congruent triangles inside an arbitrary triangle
Two congruent triangles
Intersection point of the perpendicular lines
Point of intersection of the normals
Ratio of the areas of two triangles
Segment of altitude equal to the side of the triangle
Equal sums of squares of parallelogram line segments
Point of concurrency and golden ratio
Ratio of areas
Perpendicular lines
Intersection point of three circles
Six points on conic section
Six points on an ellipse
Six concyclic points
An ellipse defined by vertices and orthocenters
Intersection point of three circles II
Intersection point of three circles III
Line segments intersecting at the nine-point center
Constant sum of triangle areas
Four concyclic points
A generalization of Napoleon's theorem
A generalization of constant chord theorem
Two triangles of equal area
An equilateral triangle whose vertices are Fermat points
Three concurrent line segments
Variations on Napoleon's theorem
Concyclic points in the plane of tangential quadrilateral
Intersection point of three circles IV
A generalization of butterfly theorem
Intersecting secants of two congruent circles
Tangent-secant theorem for two congruent circles
An ellipse determined by circumcenters
Three equilateral triangles
Characterizations of cyclic quadrilaterals
Four concyclic triangle centers
Four concyclic triangle centers II
Four concyclic triangle centers III
Four concyclic triangle centers IV
Four concyclic triangle centers V
Four concyclic triangle centers VI
Five concyclic triangle centers
Five concyclic triangle centers II
Intersection point of three circles V
Seven concyclic triangle centers
Three circles related to Conway's circle
Points of concurrency of the lines defined by triangle centers and vertices
Isosceles triangle and excircle
Area of bicentric quadrilateral
Area of bicentric pentagon
Area of bicentric hexagon
Collinearity in bicentric pentagon
Collinearity in bicentric hexagon
Parallelogram and line
Concyclicity in bicentric pentagon
Collinearity in tangential pentagon
Four orthocenters lie on a circle
Five orthocenters lie on a circle
Six orthocenters lie on a circle
Eight orthocenters lie on a circle
Collinearity in bicentric pentagon II
Six conelliptic points
Triangle and line
Parallelogram and line II
A variation on a theorem of Viviani
A variation on a theorem of Morley
Ratio of area of triangle and hexagon
Ratio of area of triangle and hexagon II
Collinearity in bicentric heptagon
Collinearity in bicentric octagon
Equal sums of line segments
Equal products of triangle areas
Three pairs of similar triangles
Four pairs of similar triangles
Principal diagonals of octagon meet in a single point
Constant product of the lengths of two line segments
A property of equilateral triangle
Sum of areas of triangles
An identity for bicentric quadrilateral
Geometrium
Author:
Poliagapitos
Topic:
Geometry
A collection of geometry propositions.
A new generalization of Bottema's theorem
Area of a rhombus
Area of a regular convex pentagon
A conic inside a hexagon
An ellipse inside a heptagon
Intersecting circles
Concurrent point in an arbitrary triangle
A generalization of Droz-Farny line theorem
Equal sums of triangle areas
A generalization of Thébault's theorem
A rhombus inside a parallelogram
Square inside a square
Equilateral triangle inside an equilateral triangle
A concyclic points inside a pentagon
Point of concurrency in an arbitrary triangle
Point of concurrency in a cyclic pentagon
Point of concurrency in a cyclic quadrilateral
Congruent triangles inside an arbitrary triangle
Two congruent triangles
Intersection point of the perpendicular lines
Point of intersection of the normals
Ratio of the areas of two triangles
Segment of altitude equal to the side of the triangle
Equal sums of squares of parallelogram line segments
Point of concurrency and golden ratio
Ratio of areas
Perpendicular lines
Intersection point of three circles
Six points on conic section
Six points on an ellipse
Six concyclic points
An ellipse defined by vertices and orthocenters
Intersection point of three circles II
Intersection point of three circles III
Line segments intersecting at the nine-point center
Constant sum of triangle areas
Four concyclic points
A generalization of Napoleon's theorem
A generalization of constant chord theorem
Two triangles of equal area
An equilateral triangle whose vertices are Fermat points
Three concurrent line segments
Variations on Napoleon's theorem
Concyclic points in the plane of tangential quadrilateral
Intersection point of three circles IV
A generalization of butterfly theorem
Intersecting secants of two congruent circles
Tangent-secant theorem for two congruent circles
An ellipse determined by circumcenters
Three equilateral triangles
Characterizations of cyclic quadrilaterals
Four concyclic triangle centers
Four concyclic triangle centers II
Four concyclic triangle centers III
Four concyclic triangle centers IV
Four concyclic triangle centers V
Four concyclic triangle centers VI
Five concyclic triangle centers
Five concyclic triangle centers II
Intersection point of three circles V
Seven concyclic triangle centers
Three circles related to Conway's circle
Points of concurrency of the lines defined by triangle centers and vertices
Isosceles triangle and excircle
Area of bicentric quadrilateral
Area of bicentric pentagon
Area of bicentric hexagon
Collinearity in bicentric pentagon
Collinearity in bicentric hexagon
Parallelogram and line
Concyclicity in bicentric pentagon
Collinearity in tangential pentagon
Four orthocenters lie on a circle
Five orthocenters lie on a circle
Six orthocenters lie on a circle
Eight orthocenters lie on a circle
Collinearity in bicentric pentagon II
Six conelliptic points
Triangle and line
Parallelogram and line II
A variation on a theorem of Viviani
A variation on a theorem of Morley
Ratio of area of triangle and hexagon
Ratio of area of triangle and hexagon II
Collinearity in bicentric heptagon
Collinearity in bicentric octagon
Equal sums of line segments
Equal products of triangle areas
Three pairs of similar triangles
Four pairs of similar triangles
Principal diagonals of octagon meet in a single point
Constant product of the lengths of two line segments
A property of equilateral triangle
Sum of areas of triangles
An identity for bicentric quadrilateral
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