Online Geometry: Triangle Centers, Theorems and Problems Index

Triangle Centers - Table of Content

	Incenter of a triangle. Index.
	Excenter. Index. Excircle, Exradius.
	Circumcenter. Index.
	Centroid /Barycenter. Index.
	Orthocenter Index.
	Circumcircle Index.
	Nine-Point Center, Nine-Point Circle, Euler Line. Interactive illustration. Circumcenter, Centroid, Orthocenter HTML5 Animation for iPad and Nexus Adobe Flash Animation.
	Gergonne Points Index Triangle Center
	Nagel Points Index Triangle Center
	Gergonne Point Theorem. Concurrency. Interactive proof with animation. HTML5 Animation for Tablets (iPad, Nexus) Adobe Flash Animation Key concept: Ceva's Theorem.
	Nagel Point Theorem. Proof.
	Symmedian (Lemoine) Point Triangle Center
	Fermat Point.
	Outer Vecten Point.
	Morley's Triangle and Center Triangle Center
	Feuerbach Point Triangle Center
	iPad Apps: Apollonius Software. Feuerbach Point. Triangle, Incircle, Nine point circle, Tangent circles, Orthocenter, Midpoint. Interactive Geometry Software.
	Schiffler Point: Euler Lines Triangle Center
	The Bevan Point The circumcenter of the excentral triangle. Illustration with animation.
	Spieker Center Triangle Center
	Ajima-Malfatti Point 2 Triangle Center. Interactive illustration.
	Ajima-Malfatti Point 1 Triangle Center. Interactive illustration.
	Steiner Point Triangle Center
	Mittenpunkt Point Triangle Center
	Kosnita's Theorem. Circumcenters, Concurrent lines.
	Clawson Point. Orthic and Extangents Triangles, Concurrent lines.
	Clawson Point Puzzle, Geometry for Kids. 22 Piece Polygons
	Adams' Circle Theorem
	Distances between Triangle Centers Index.
	Triangle Centers, Visual Index.
	Triangle Centers.
	Proposed Problem 246. Napoleon's Theorem I. External Equilateral triangles.
	Circulo de los Nueve Puntos: Spanish version. Interactive illustration.
	Puzzle: Euler Line and Nine Point Center
	Geometry Problem 821. Adams Circle.
	Geometry Problem 754. Equilateral Triangle, Center, Angle, 60 Degrees, Perimeter.
	Problem 690: Distance between the Incenter and the Centroid of a Triangle. Formula in terms of the sides a,b,c.
	Geometry Problem 689. Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines, Mind Map.
	Proposed Problem 370. Triangle with squares, Circumcircles, Tangent circles.
	Equal Incircles Theorem: Triangles, cevians, circles.
	Proposed Problem 257. Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.
	Proposed Problem 256. Equilateral Triangle, Circumcircle, Point, Vertices, Distances.
	Proposed Problem 255. Triangle, Centroid, Vertices, a Point, Distances, Squares.
	Proposed Problem 254. Triangle, Centroid, Vertices, a Point, Distances, Squares.
	Proposed Problem 253. Triangle, Centroid, Vertices, Distances, Squares.
	Proposed Problem 249. Triangle sides, medians, squares.
	Proposed Problem 248. Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.
	Proposed Problem 247. Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon triangle.
	Proposed Problem 229. Triangle, Centroid, Transversal, Perpendicular lines.
	Proposed Problem 226. Triangle, Centroid, Perpendicular lines.
	Proposed Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.
	Proposed Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.
	Proposed Problem 196. Triangle, Inradius and Exradii Formula.
	Journey to the Center of a Triangle (1976). Incenter, Circumcenter, Centroid, Orthocenter.
	Proposed Problem 213. Triangle, Incircle, Inradius, Semicircles, Common Tangents.
	Proposed Problem 209. Triangle, Incircles, Inradius.
	Proposed Problem 208. Triangle, Excircles, Angles, 360 degrees.
	Proposed Problem 207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse.
	Problem 206. Area of a Right Triangle, Inradius, andExradius relative to the hypotenuse.
	Proposed Problem 205. Right Triangle Area, Exradii relatives to legs or catheti.
	Proposed Problem 204. Right Triangle, Incircle, Excircles, Inradius, Exradii.
	Proposed Problem 203. Right Triangle, Excircles, Exradii, Hypotenuse.
	Proposed Problem 202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter.
	Proposed Problem 20 1. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter.
	Proposed Problem 200. RightTriangle, Incircle, Excircles, Points of Tangency, Inradius.
	Proposed Problem 197. Area of a Triangle, Side, Inradius, and Exradius.
	Proposed Problem 196. Triangle, Inradius and Exradii Formula.
	Proposed Problem 195. Area of a Triangle, Inradius, Exradii.
	Proposed Problem 194. Area of a Triangle, Semiperimeter, Exradius.
	Proposed Problem 193. Area of a Triangle, Semiperimeter, Inradius.
	Proposed Problem 191. Triangle, Altitudes, Orthocenter, Squares, Areas.
	Puzzle of the Nagel Point: 22 pieces of polygons.
	Nagel Point Theorem - Flowchart Proof .
	Semiperimeter and excircles of a triangle.
	Semiperimeter and incircle of a triangle.
	Semiperimeter, incircle and excircles of a triangle.
	Gergonne Point Theorem. Concurrency. Interactive proof with animation. Key concept: Ceva's Theorem.
	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 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.
	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 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 13 7. 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.
	Interactive Gergonne Line and Nobbs Points. Dynamic Geometry. Step-by-Step construction, Manipulation, and animation.
	Triangle, Medians, Six Circumcenters Concyclic. Dynamic Geometry. Step-by-Step construction, Manipulation, and animation. Prove proposition.
	Triangle: Incircle, Perpendicular, Angle Bisector. Dynamic Geometry. Step-by-Step construction, Manipulation, and animation. Prove proposition.
	Proposed Problem 133. Triangle, Angle Bisectors, Collinear Points.
	Proposed Problem 132. Triangle, 60 degree, Orthocenter, Congruence, Midpoint.
	Triangle with the bisectors of the exterior angles. Collinearity. Key concept: Menelaus Theorem.
	Proposed Problem 128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.
	Proposed Problem 127. Centroid and Incenter of a Triangle, Parallel, Proportions.
	Proposed Problem 126. Incenter of Triangle, Angle Bisector, Proportions.
	Proposed Problem 120. Area of triangle, incenter, excircles, tangent.
	Proposed Problem 119. Area of triangle, incenter, excircle, tangent.
	Proposed Problem 118. Area of triangle, incenter, excenter, tangent.
	Proposed Problem 117. Area of triangle, incenter, excircles, tangent.
	Proposed Problem 116. Area of triangle, excircles, tangent.
	Proposed Problem 115. Area of triangle, excircles, tangent.
	Proposed Problem 114. Area of triangle, incircle, excircle.
	Proposed Problem 113. Area of triangle, incircle, excircle.
	Complete Quadrilateral: Ortholine-Steiner Line. Using TracenPoche Dynamic Software Step-by-Step construction, Manipulation, and animation
	Proposed Problem 96. Similar Triangles, Incenters, Parallelogram.
	Proposed Problem 95. Similar Triangles, Inradii, Parallel.
	Proposed Problem 94. Similar Triangles, Circumcircles, Circumradii.
	Proposed Problem 93. Similar Triangles, Circumcircles, Parallelogram.
	Proposed Problem 92. Similar Triangles, Circumcircles, Circumradii, Parallel.
	Intouch and Extouch Triangles. Puzzle cut: 20 Piece Classic Based on Proposed Problem 86.
	Proposed Problem 86. Intouch and Extouch Triangles, Areas.
	Contact Triangles. Puzzle cut: 22 Piece Polygons Based on Proposed Problem 85.
	Proposed Problem 85. Contact Triangles Areas, Incircle, Excircle.
	Proposed Problem 84. Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius.
	Proposed Problem 83. Area of the Excircle Contact Triangle, exradius, circumradius.
	Proposed Problem 82. Area of the Contact Triangle, inradius, circumradius.
	Proposed Problem 81. Area of a triangle, side, inradius, circumradius.
	Proposed Problem 80. Area of a triangle, side, incircle, inradius.
	Proposed Problem 79: Triangle. Similarity, Altitudes, Orthocenter, Incircles, Inradii.
	Interactive Orthopole of a Triangle: Using TracenPoche Dynamic Geometry Software, Online Step-by-Step construction, manipulation, and animation.
	Morley's Triangle & Center: with interactive animation and manipulation.
	Schiffler Point: Four Euler Lines with interactive animation and manipulation.
	Proposed Problem 68: Triangle, Incircle, Inradius, Tangent, Similarity.
	Proposed Problem 67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
	Proposed Problem 66: Triangle, Excircle, Tangents, Geometric Mean.
	Proposed Problem 64: Triangle, Incircle, Transversal.
	Incenter, Excenter, Incircle, Excircle Using TracenPoche Dynamic Software Step-by-Step construction, Manipulation, and animation.
	Three Tangent Circles Theorem Using TracenPoche Dynamic Software Step-by-Step construction, Manipulation, and animation.
	Sangaku Geometry Theorem: Cyclic Quadrilateral. Inradii, Rectangle.
	Sangaku Problem (An Old Japanese Theorem). Inradii, Carnot's theorem.
	Triangle Centers. Word find puzzle.
	Proposed Problem 52: Triangle, angles, incircle.
	Feuerbach Theorem One of the most striking theorems in triangle geometry.
	Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.
	Feuerbach Point Facts
	Feuerbach Theorem, Acute Triangle illustration
	Feuerbach Theorem, Obtuse Triangle illustration
	Feuerbach Theorem, Right Triangle illustration
	Proposed Problem 51: Fagnano's Problem Inscribed Triangle with the Minimum Perimeter.
	Proposed Problem 40. Triangle, Incenter, Excenter, Angles 80, 40, Distances.
	Proposed Problem 40. Geometry Help.
	Proposed Problem 39. Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles.
	Proposed Problem 39 Geometry Help. Facts you should know for the proposed problem 39.
	Proposed Problem 38. Right Triangle, altitude, incircles, incenters, and angles.
	Proposed Problem 37. Right Triangle, altitude, incircles, incenters, and orthocenter.
	Proposed Problem 36. Right Triangle, altitude, incircles and inradii.
	Lemoine Theorem
	Triangle and Squares 17
	Triangle and Squares 16
	Sawayama -Thebault's theorem
	Proposed Problem 34. Right triangle, cevian, incircles, tangents and inradius.
	Problem 32. Triangle, Cevian, Incircles, Tangents.
	Problem 31. Right Triangle, Incircle, Collinears. Problem 30. Right Triangle, Incircle, Inradius.
	Proposed Problem 29. Right Triangle, altitude, incircle and inradius. Ten conclusions.
	Problem 29: Geometry Help. Facts you should know.
	Heron's Formula with medians
	Proposed Problem 28 Right Triangle, altitude, incircles and inradius.
	Proposed Problem 27 Right Triangle, incircles and inradius.
	Proposed Problem 26 Right Triangle, altitude, incircles and inradius.
	Proposed Problem 25 Right Triangle, altitude, incircles and inradius.
	Proposed Problem 24 Right Triangle, altitude, incircles and inradii.
	Proposed Problem 23 Right Triangle, altitude, incircles and inradii.
	Proposed Problem 22 Right Triangle, altitudes, incircles and inradii.
	Proposed problem 21 Acute triangle, orthocenter, diameter, tangents.
	Proposed problem 20 Right Triangle, incircles and inradii.
	Proposed problem 19 Right Triangle and Excenter
	Heron's Formula. Key facts and a purely geometric step-by-step proof.
	Napoleon's Theorem. A purely geometric proof. It uses the Fermat point to prove Napoleon without transformations.
	The Bevan Point: Puzzle

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