Geometry Theorems and Problems - Recent Additions (Page
11 of 15)
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![Euclidean Geometry](euclidean_geometry_17.jpg) |
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![Elearning 190 tangent circles, chord, perpendicular](../problem/p190_tangent_circles_17.jpg) |
Proposed Problem
190. Tangent circles, Tangent chord, Perpendicular, Distance.
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![Elearning 189](../problem/p189_square_fact_17.jpg) |
Proposed Problem
189. Squares, Distances.
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![Elearning 188](../problem/p188_square_45_degree_17.gif) |
Proposed Problem
188. Square, Diagonal, 45 Degrees Angle.
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![Elearning 187: Right triangle, incircles, angles](../problem/p187_right_triangle_17.jpg) |
Proposed Problem
187. Right Triangle, Altitude, Incenters, Circles,
Angles. |
![Elearning 186: Right triangle, circles](../problem/p186_right_triangle_17.jpg) |
Proposed Problem
186. Right Triangle, Altitude, Incenters, Circles. |
![Elearning 186: Right triangle, circles](../problem/p186_right_triangle_17.jpg) |
Proposed Problem
186. Right Triangle, Altitude, Incenters, Circles. |
![Trapezoid and triangle problem](../problem/p185_trapezoid_angle_17.jpg) |
Proposed Problem
185. Trapezoid, Triangles and Angles.
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![Elearning: Triangle, Angle](../problem/p184_triangle_angle_17.jpg) |
Proposed Problem
184. Triangle and Angles.
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![Right triangle, Hypotenuse trisection](../problem/p183_right_triangle_17.jpg) |
Proposed Problem
183. Right Triangle, Hypotenuse Trisection Points, Squares of the Distances.
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![Overlapping circles, Angle](../problem/p182_overlapping_circles_17.jpg) |
Proposed Problem
182. Overlapping Circles, Find an angle.
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![Circular Sector 90 degree](../problem/p181_circular_sector_90_17.jpg) |
Proposed Problem
181. Circular Sector of 90 degrees, find an angle.
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![Circle tangent externally, trapezoid, area](../problem/p180_circle_trapezoid_area_.jpg) |
Proposed Problem
180. Circles Tangent Externally, Common External Tangents, Areas.
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![Rhombus, Square, Angle](../problem/p179_rhombus_square_17.jpg) |
Proposed Problem
179. Rhombus, Square, Diagonal, Angle.
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![Geometry problem 178 Quadrilateral area](../problem/p178_quadrilateral_area_17.jpg) |
Proposed Problem
178. Quadrilateral, Trisection of sides, Area.
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![Elearning 177: Parallelogram with midpoints, Area](../problem/p177_parallelogram_area_17.jpg) |
Proposed Problem
177. Parallelogram with Midpoints,
Triangles, Areas. |
![Elearning 176: Quadrilateral Area Problem](../problem/p176_quadrilateral_area_17.jpg) |
Proposed Problem
176. Quadrilateral with Midpoints,
Triangles, Areas.
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![Elearning 175: Quadrilateral Area Problem](../problem/p175_quadrilateral_area_17.jpg) |
Proposed Problem
175. Quadrilateral with Midpoints, Areas.
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![Quadrilateral with Midpoints, Triangles Area](../problem/p174_quadrilateral_area_17.jpg) |
Proposed Problem
174. Quadrilateral with Midpoints, Triangles, Areas.
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![Quadrilateral with Midpoints, Triangles Area](../problem/p173_quadrilateral_area_17.jpg) |
Proposed Problem
173. Quadrilateral with Midpoints, Triangles, Areas.
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![Elearning 172: Trapezoid, Quadrilateral, Area](../problem/p172_trapezoid_quadrilatera.jpg) |
Proposed Problem
172. Trapezoid, Midpoints, Quadrilaterals, Areas.
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![Elearning 172: Trapezoid, Midpoints, Quadrilaterals, Areas](../problem/p171_trapezoid_triangle_17.jpg) |
Proposed Problem
171. Trapezoid, Midpoints, Triangles, Areas.
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![Trapezoid, Triangle, Area](../problem/p170_trapezoid_triangle_17.jpg) |
Proposed Problem
170. Trapezoid, Midpoint, Triangle, Area.
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![Geometry Problem: Parallelogram, Triangles, Pentagon, Area](../problem/p169_parallelogram_area_17.jpg) |
Proposed Problem
169. Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas
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![Geometry Problem: Parallelogram, Triangles, Pentagon, Area](../problem/p168_parallelogram_area_17.jpg) |
Proposed Problem
168. Parallelogram, Diagonal, Triangles,
Pentagon, Areas.
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![Geometry Problem: Parallelogram, Triangles, Area](../problem/p167_parallelogram_area_17.jpg) |
Proposed Problem
167. Parallelogram, Diagonal, Triangles, Areas.
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![Geometry Problem: Parallelogram, Triangles, Area](../problem/p166_parallelogram_area_17.jpg) |
Proposed Problem
166. Parallelogram, Diagonal, Triangles, Areas.
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![Elearning 165: Parallelogram area](../problem/p165_parallelogram_area_17.jpg) |
Proposed Problem
165. Parallelogram, Diagonal, Triangles, Areas.
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![Elearning 164: Parallelogram, Triangles, Area](../problem/p164_parallelogram_area_17.jpg) |
Proposed Problem
164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas.
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![Elearning 163 Trapezoid, Triangles, Area](../problem/p163_trapezoid_triangle_17.jpg) |
Proposed Problem
163. Trapezoid, Diagonals, Triangles, Areas.
Trapezoid Index |
![Elearning 162 Parallelogram and Triangles Areas](../problem/p162_parallelogram_area_17.jpg) |
Proposed Problem
162. Parallelogram, Triangles, Areas.
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![Elearning 161 Parallelogram and Octagon Areas](../problem/p161_parallelogram_area_17.jpg) |
Proposed Problem
161. Parallelogram, Midpoints, Octagon, Areas.
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![Elearning: Triangle, Circle, Incircle, Radius](../problem/p160_elearning_triangle_17.jpg) |
Proposed Problem 160. Triangle,
Incircle, Incenter, Circumcircle, Circumcenter, Inradius. |
![Triangle Elearning 159](../problem/p159_elearning_triangle_17.jpg) |
Proposed Problem 159. Distances
from the Circumcenter to the Incenter and the Excenters. |
![Geometry Problem 158](../problem/p158_elearning_triangle_17.jpg) |
Proposed Problem 158. Relation
between the Circumradius, Inradius and Exradii of a triangle. |
![Areas](areas_measurement_17.jpg) |
Areas Index. |
![Congruence](congruence_geometry_17.jpg) |
Congruence. Index.
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![Similarity](similarity_ratio_index_17.jpg) |
Similarity, Ratios, Proportions.
Index.
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![Elearning triangle 157](../problem/p157_elearning_triangle_17.jpg) |
Proposed Problem 157. Distance
from the Circumcenter to the Excenter. |
![Elearning triangle 156](../problem/p156_elearning_triangle_17.jpg) |
Proposed Problem 156. Triangle,
Circumradius, Exradius, Chord, Secant line. |
![Elearning 155](../problem/p155_triangle_circle_17.jpg) |
Proposed Problem 155. Euler's
Theorem: Distance from the Incenter to the Circumcenter. |
![Elearning 154](../problem/p154_triangle_circle_17.jpg) |
Proposed Problem 154. Triangle,
Inradius, Circumradius, Chord. |
![Circumscribed quadrilateral](../problem/p153_quadrilateral_circle_1.jpg) |
Proposed Problem 153.
Circumscribed Quadrilateral, Diagonals Concurrent with Chords.
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![Circumscribed Quadrilateral](../problem/p152_circumscribed_17.jpg) |
Proposed Problem 152.
Circumscribed Quadrilateral, Diagonal, Chord, Proportion.
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![Quadrilateral area, trisection](../problem/p151_quadrilateral_area_17.jpg) |
Proposed Problem 151.
Quadrilateral, Area, Trisection of Sides.
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![Quadrilateral area, trisection](../problem/p150_quadrilateral_area_17.jpg) |
Proposed Problem 150.
Quadrilateral, Area, Trisection of Sides.
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![Quadrilateral Area, Midpoint, Elearning](../problem/p149_quadrilateral_area_17.jpg) |
Proposed Problem 149.
Quadrilateral, Area, Midpoints.
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![Quadrilateral area, Midpoint, Elearning](../problem/p148_quadrilateral_area_17.jpg) |
Proposed Problem 148.
Quadrilateral, Area, Midpoints.
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![Quadrilateral Area, Elearning](../problem/p147_quadrilateral_area_17.jpg) |
Proposed Problem 147.
Quadrilateral, Area, Midpoints, Triangle.
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![Quadrilateral Area, Midpoint](../problem/p146_quadrilateral_area_17.jpg) |
Proposed Problem 146. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter. |
![Geometry Problem 145. Elearning Triangle](../problem/p145_four_triangles_circle_.jpg) |
Proposed Problem 145. Four
Triangles, Incircle, Tangent and Parallel to Side, Incenters,
Circumcenters. |
![Geometry problem 144 Triangle](../problem/p144_four_triangles_circle_.jpg) |
Proposed Problem 144. Four
Triangles, Incircle, Tangent and Parallel to Side, Inradii. |
![Geometry problem 143](../problem/p143_four_triangles_circle_.jpg) |
Proposed Problem 143. Four
Triangles, Incircle, Tangent and Parallel to Side, Circumradii. |
![Elearning 142: Triangle area](../problem/p142_four_triangles_area_17.jpg) |
Proposed Problem 142. Four
Triangles, Incircle, Tangent and Parallel to Side, Areas. |
![Elearning 141](../problem/p141_four_triangles_incircl.jpg) |
Proposed Problem 141. Triangle,
Incircle, Tangent , Parallel, Perimeters. |
![Elearning 140](../problem/p140_triangle_excircle_17.jpg) |
Proposed Problem 140. Triangle,
Excircle, Tangent, Semiperimeter. |
![Elearning 139: Triangle Area](../problem/p139_area_triangle_17.jpg) |
Proposed Problem 139. Triangle
Area, Orthic Triangle, Semiperimeter, Circumradius. |
![Nagel Theorem](../problem/p138_nagel_theorem_17.jpg) |
Proposed Problem 138. Nagel's
Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular.
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![Geometry Problem 137](../problem/p137_orthic_triangle_17.jpg) |
Proposed Problem 137.
Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points,
Parallelogram. |
![Geometry Problem 136](../problem/p136_orthic_triangle_17.jpg) |
Proposed Problem 136. Orthic
Triangle, Altitudes, Perpendicular, Concyclic Points. |
![Geometry Problem 135](../problem/p135_orthic_triangle_17.jpg) |
Proposed Problem 135. Orthic
Triangle, Altitudes, Perpendicular, Parallel |
![Geometry Problem 134](../problem/p134_orthic_triangle_17.jpg) |
Proposed Problem 134. Orthic
Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter. |
![Pappus Theorem](pappus_theorem_17.jpg) |
Pappus Theorem. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation. |
![Gergonne Line](gergonne_line_17.jpg) |
Interactive
Gergonne Line and Nobbs Points.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation. |
![Interactive Simson Line](interactive_simson_line_17.jpg) |
Interactive Simson
Line. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation. |
![Elearning Geometry](triangle_median_circ_17.jpg) |
Triangle,
Medians, Six Circumcenters Concyclic.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
![Trapezoid](trapezoid_diagonal_01_17.jpg) |
Trapezoid,
Triangle, Diagonals, Midpoints.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
![Interactive Geometry](triangle_incircle_perpendic.jpg) |
Triangle: Incircle, Perpendicular, Angle Bisector.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
![Problem 133](../problem/p133_angle_bisector_17.jpg) |
Proposed Problem 133. Triangle,
Angle Bisectors, Collinear Points.
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![](../triangles_170.jpg) |
Triangles.
Theorems and problems about triangles. |
![](../circles_170.jpg) |
Circles.
Theorems and problems about circles. |
![](../triangle_center_170.jpg) |
Triangle Centers. |
![](../ArchBooLem04_170.jpg) |
Archimedes' Book
of Lemmas
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![](../triangle_square/machu_picchu_quad_170.jpg) |
Quadrilaterals.
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![](../circle/adams_circle_theorem_170.jpg) |
Adams' Circle Theorem. |
![](../center/ajima_malfatti_170.jpg) |
First Ajima-Malfatti Point. |
![](../center/ajima_malfatti_170_2.jpg) |
Second Ajima-Malfatti
Point. |
![](../circle/apollonius_problem_circle_1.jpg) |
Apollonius' Tangency Problem for Three Circles
Illustration with animation.
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![](../Bevan170.jpg) |
The
Bevan Point.
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![](../heron/heron__proof_170x100.jpg) |
Heron's Formula. Key facts and
a purely geometric
step-by-step proof.
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![Johnson: Intersecting circles](../johnson170x100.jpg) |
Johnson Theorem. |
![](../Kurschak170x100.jpg) |
Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 1864-1933) A square, with equilateral triangles. An elegant and a purely geometric
way of finding the area of a regular dodecagon.
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![](../langley170x100.jpg) |
Langley's
Problem Adventitious
angles. 20° isosceles triangle with animation.
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![](../problem/lemoine_theorem_170.jpg) |
Lemoine Theorem |
![](../menelaus170x100.jpg) |
Menelaus' Theorem. |
![Miquel's Pentagram Theorem](../miquel100.jpg) |
Miquel's Pentagram Theorem
Interactive proof with animation and key theorems.
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![](../javacar/miquel_pentagram_170.jpg) |
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 Plug-in 1.3 or higher. Please be patient while
the applet loads on your computer. |
![](../javacar/monge_2_dynamic_170.jpg) |
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
Plug-in 1.3 or higher. Please be patient while
the applet loads on your computer. |
![](../javacar/monge_1_dynamic_170.jpg) |
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
Plug-in 1.3 or higher. Please be patient while
the applet loads on your computer. |