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Area of a triangle, Theorems and Problems - Table of Content
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Heron's Formula.
Key facts and
a purely geometric
step-by-step proof.
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Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and
trisection points of the edges. Triangle areas.
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Routh's Theorem - Index
Triangle, Cevians, Area, Ratio.
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Marion Walter's Theorem
and Related Topics: Index |
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Proposed
Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity. |
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Proposed
Problem 416.
Triangle, Cevians, Trisectors, Area. |
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Proposed
Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence. |
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Proposed
Problem 371.
Square, Inscribed circle, Triangle, Area. |
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Proposed
Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area. |
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Proposed
Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters. |
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Proposed
Problem 357.
Square, Exterior point, Triangles, Area. |
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Proposed
Problem 356.
Square, Point inside, Triangles, Area. |
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Proposed Problem
322.
Square, Inscribed circle, Tangent, Triangle area. |
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Proposed Problem
273.
Triangle, Perpendiculars, Area of Squares. |
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Proposed Problem
252.
Rectangle, isosceles right triangle, square, area.
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Proposed Problem
248.
Napoleon's Theorem III. Inner and outer Napoleon triangles areas.
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Proposed Problem
225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance.
Area of triangles. |
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Proposed Problem
224. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Point on the extension of the base. Area of
triangles. |
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Proposed Problem
223. Viviani's theorem, Isosceles triangle,
Altitude, Distances. Area of triangles. |
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Proposed Problem
222. Viviani's theorem, Equilateral triangle, Exterior point,
Distances. Area of triangles. |
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Proposed Problem
221. Viviani's theorem, Equilateral triangle, Interior point,
Distances. Area of triangles. |
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Lune of Hippocrates Index.
Area of a right triangle. |
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Proposed Problem
212. 120 Degree Triangle, Equilateral triangles, Areas.
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Proposed Problem
211. 60 Degree Triangle, Equilateral triangles, Areas.
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Proposed Problem
206. Area of a Right Triangle, Inradius, and Exradius relative to the hypotenuse. |
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Proposed Problem
205. Right Triangle Area, Exradii relatives to legs or catheti. |
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Proposed Problem
197. Area of a Triangle, Side, Inradius, and Exradius. |
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Proposed Problem
196. Area of triangles, Inradius and Exradii Formula. |
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Proposed Problem
195. Area of a Triangle, Inradius, Exradii. |
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Proposed Problem
194. Area of a Triangle, Semiperimeter, Exradius. |
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Proposed Problem
193. Area of a Triangle, Semiperimeter, Inradius. |
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Proposed Problem
192. Circle, Diameter, Chord, Perpendicular, Triangle, Area.
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Proposed Problem
191. Triangle, Altitudes, Orthocenter, Squares, Areas.
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Proposed Problem
180. Circles Tangent Externally, Common External Tangents,
Triangle Areas.
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Proposed Problem
177. Parallelogram with Midpoints,
Triangles, Areas. |
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Proposed Problem
176. Quadrilateral with Midpoints,
Triangles, Areas.
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Proposed Problem
174. Quadrilateral with Midpoints, Triangles, Areas.
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Proposed Problem
173. Quadrilateral with Midpoints, Triangles, Areas.
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Proposed Problem
172. Trapezoid, Midpoints, Quadrilaterals, Areas.
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Proposed Problem
171. Trapezoid, Midpoints, Triangles, Areas.
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Proposed Problem
170. Trapezoid, Midpoint, Triangle, Area.
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Proposed Problem
169. Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas
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Proposed Problem
168. Parallelogram, Diagonal, Triangles,
Pentagon, Areas.
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Proposed Problem
167. Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem
166. Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem
165. Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem
164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas.
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Proposed Problem
163. Trapezoid, Diagonals, Triangles, Areas.
Trapezoid Index |
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Proposed Problem
162. Parallelogram, Triangles, Areas.
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Proposed Problem
161. Parallelogram, Midpoints,
Area of an Octagon, Area of triangles.
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Proposed Problem
147. Quadrilateral, Area, Midpoints, Triangle.
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Proposed Problem
146. Varignon's Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter.
Triangles. |
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Proposed Problem
142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas. |
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Proposed Problem
139. Triangle Area, Orthic Triangle, Semiperimeter, Circumradius. |
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Proposed Problem
125. Area of Triangle, Star,
Trisection of Sides.
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Proposed Problem
124. Area of triangle,
Similarity, Trisection of Sides.
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Proposed Problem
123. Area of triangle,
Similarity, Trisection of Sides.
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Proposed Problem
122. Marion Walter's Theorem.
Area of triangle and Hexagon, Trisection of Sides.
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Proposed Problem
121. Similarity and Area
of triangle, Trisection of Sides.
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Proposed Problem
120. Area of triangle,
incenter, excircles,
tangent.
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Proposed Problem
119. Area of triangle,
incenter, excircle,
tangent.
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Proposed Problem
118. Area of triangle,
incenter, excenter,
tangent.
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Proposed Problem
117. Area of triangle,
incenter, excircles,
tangent.
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Proposed Problem
116. Area of triangle, excircles,
tangent.
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Proposed Problem
115. Area of triangle, excircles,
tangent.
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Proposed Problem
114. Area of triangle, incircle,
excircle.
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Proposed Problem
113. Area of triangle, incircle,
excircle.
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Proposed Problem
112. Area of square and triangle.
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Proposed Problem
110. Area of Contact Triangle.
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The Pythagorean Curiosity
Triangles and squares, fifteen conclusions. |
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Proposed Problem
103.Equilateral Triangle Area,
Interior Point, Heron's Formula.
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Proposed Problem
102.Equilateral Triangle Area,
Interior Point. |
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Proposed Problem
97. Similar Triangles, Areas. |
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Proposed Problem
90. Quadrilateral and Triangle
Areas, Midpoints. |
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Proposed Problem
89. Triangles of equal area, Midpoints. |
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Proposed Problem
88. Triangle and Quadrilateral Areas, Midpoints. |
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Proposed Problem
87. Area of Quadrilaterals and Midpoints of Diagonals.
Area of triangles. |
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Proposed Problem
86. Intouch and Extouch Triangles, Areas. |
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Proposed Problem
85. Contact Triangles Areas, Incircle, Excircle. |
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Proposed Problem
84. Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius. |
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Proposed Problem
83. Area of the Excircle Contact
Triangle, exradius, circumradius. |
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De Gua's Theorem
Area of triangles. |
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Triangle and Squares 22
Area of triangles and rectangles.
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Hippocrates
and Squaring the Circle
Triangle areas |
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Heron's Formula
with medians Triangle
areas. |
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Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.
Triangle areas. |
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Euclid's Elements
Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book.
Index |
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Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and
trisection points of the edges. Triangle areas.
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