Geometry Theorems and Problems  Recent Additions (Page
11 of 15)




Proposed Problem
190. Tangent circles, Tangent chord, Perpendicular, Distance.


Proposed Problem
189. Squares, Distances.


Proposed Problem
188. Square, Diagonal, 45 Degrees Angle.


Proposed Problem
187. Right Triangle, Altitude, Incenters, Circles,
Angles. 

Proposed Problem
186. Right Triangle, Altitude, Incenters, Circles. 

Proposed Problem
186. Right Triangle, Altitude, Incenters, Circles. 

Proposed Problem
185. Trapezoid, Triangles and Angles.


Proposed Problem
184. Triangle and Angles.


Proposed Problem
183. Right Triangle, Hypotenuse Trisection Points, Squares of the Distances.


Proposed Problem
182. Overlapping Circles, Find an angle.


Proposed Problem
181. Circular Sector of 90 degrees, find an angle.


Proposed Problem
180. Circles Tangent Externally, Common External Tangents, Areas.


Proposed Problem
179. Rhombus, Square, Diagonal, Angle.


Proposed Problem
178. Quadrilateral, Trisection of sides, Area.


Proposed Problem
177. Parallelogram with Midpoints,
Triangles, Areas. 

Proposed Problem
176. Quadrilateral with Midpoints,
Triangles, Areas.


Proposed Problem
175. Quadrilateral with Midpoints, Areas.


Proposed Problem
174. Quadrilateral with Midpoints, Triangles, Areas.


Proposed Problem
173. Quadrilateral with Midpoints, Triangles, Areas.


Proposed Problem
172. Trapezoid, Midpoints, Quadrilaterals, Areas.


Proposed Problem
171. Trapezoid, Midpoints, Triangles, Areas.


Proposed Problem
170. Trapezoid, Midpoint, Triangle, Area.


Proposed Problem
169. Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas


Proposed Problem
168. Parallelogram, Diagonal, Triangles,
Pentagon, Areas.


Proposed Problem
167. Parallelogram, Diagonal, Triangles, Areas.


Proposed Problem
166. Parallelogram, Diagonal, Triangles, Areas.


Proposed Problem
165. Parallelogram, Diagonal, Triangles, Areas.


Proposed Problem
164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas.


Proposed Problem
163. Trapezoid, Diagonals, Triangles, Areas.
Trapezoid Index 

Proposed Problem
162. Parallelogram, Triangles, Areas.


Proposed Problem
161. Parallelogram, Midpoints, Octagon, Areas.


Proposed Problem 160. Triangle,
Incircle, Incenter, Circumcircle, Circumcenter, Inradius. 

Proposed Problem 159. Distances
from the Circumcenter to the Incenter and the Excenters. 

Proposed Problem 158. Relation
between the Circumradius, Inradius and Exradii of a triangle. 

Areas Index. 

Congruence. Index.


Similarity, Ratios, Proportions.
Index.


Proposed Problem 157. Distance
from the Circumcenter to the Excenter. 

Proposed Problem 156. Triangle,
Circumradius, Exradius, Chord, Secant line. 

Proposed Problem 155. Euler's
Theorem: Distance from the Incenter to the Circumcenter. 

Proposed Problem 154. Triangle,
Inradius, Circumradius, Chord. 

Proposed Problem 153.
Circumscribed Quadrilateral, Diagonals Concurrent with Chords.


Proposed Problem 152.
Circumscribed Quadrilateral, Diagonal, Chord, Proportion.


Proposed Problem 151.
Quadrilateral, Area, Trisection of Sides.


Proposed Problem 150.
Quadrilateral, Area, Trisection of Sides.


Proposed Problem 149.
Quadrilateral, Area, Midpoints.


Proposed Problem 148.
Quadrilateral, Area, Midpoints.


Proposed Problem 147.
Quadrilateral, Area, Midpoints, Triangle.


Proposed Problem 146. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter. 

Proposed Problem 145. Four
Triangles, Incircle, Tangent and Parallel to Side, Incenters,
Circumcenters. 

Proposed Problem 144. Four
Triangles, Incircle, Tangent and Parallel to Side, Inradii. 

Proposed Problem 143. Four
Triangles, Incircle, Tangent and Parallel to Side, Circumradii. 

Proposed Problem 142. Four
Triangles, Incircle, Tangent and Parallel to Side, Areas. 

Proposed Problem 141. Triangle,
Incircle, Tangent , Parallel, Perimeters. 

Proposed Problem 140. Triangle,
Excircle, Tangent, Semiperimeter. 

Proposed Problem 139. Triangle
Area, Orthic Triangle, Semiperimeter, Circumradius. 

Proposed Problem 138. Nagel's
Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular.


Proposed Problem 137.
Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points,
Parallelogram. 

Proposed Problem 136. Orthic
Triangle, Altitudes, Perpendicular, Concyclic Points. 

Proposed Problem 135. Orthic
Triangle, Altitudes, Perpendicular, Parallel 

Proposed Problem 134. Orthic
Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter. 

Pappus Theorem. Dynamic Geometry.
StepbyStep construction, Manipulation, and animation. 

Interactive
Gergonne Line and Nobbs Points.
Dynamic Geometry.
StepbyStep construction, Manipulation, and animation. 

Interactive Simson
Line. Dynamic Geometry.
StepbyStep construction, Manipulation, and animation. 

Triangle,
Medians, Six Circumcenters Concyclic.
Dynamic Geometry.
StepbyStep construction, Manipulation, and animation.
Prove proposition. 

Trapezoid,
Triangle, Diagonals, Midpoints.
Dynamic Geometry.
StepbyStep construction, Manipulation, and animation.
Prove proposition. 

Triangle: Incircle, Perpendicular, Angle Bisector.
Dynamic Geometry.
StepbyStep construction, Manipulation, and animation.
Prove proposition. 

Proposed Problem 133. Triangle,
Angle Bisectors, Collinear Points.


Triangles.
Theorems and problems about triangles. 

Circles.
Theorems and problems about circles. 

Triangle Centers. 

Archimedes' Book
of Lemmas


Quadrilaterals.


Adams' Circle Theorem. 

First AjimaMalfatti Point. 

Second AjimaMalfatti
Point. 

Apollonius' Tangency Problem for Three Circles
Illustration with animation.


The
Bevan Point.


Heron's Formula. Key facts and
a purely geometric
stepbystep proof.


Johnson Theorem. 

Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 18641933) A square, with equilateral triangles. An elegant and a purely geometric
way of finding the area of a regular dodecagon.


Langley's
Problem Adventitious
angles. 20° isosceles triangle with animation.


Lemoine Theorem 

Menelaus' Theorem. 

Miquel's Pentagram Theorem
Interactive proof with animation and key theorems.


Miquel's
Pentagram with Dynamic Geometry.
You can alter the pentagram dynamically
in order to test and prove (or disproved) conjectures and gain
mathematical insight that is less readily available with static drawings
by hand. Requires Java Plugin 1.3 or higher. Please be patient while
the applet loads on your computer. 

Monge &
d'Alembert Three Circles Theorem II with Dynamic Geometry. You can alter the geometric construction dynamically in order to test
and prove (or disproved) conjectures and gain mathematical insight that
is less readily available with static drawings by hand. Requires Java
Plugin 1.3 or higher. Please be patient while
the applet loads on your computer. 

Monge &
d'Alembert Three Circles Theorem I with Dynamic Geometry. You can alter the geometric construction dynamically in order to test
and prove (or disproved) conjectures and gain mathematical insight that
is less readily available with static drawings by hand. Requires Java
Plugin 1.3 or higher. Please be patient while
the applet loads on your computer. 