

Geometry: Incenter, Incircle, Inradius of a triangle, Theorems
and Problems.




Proposed Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle. 

Proposed Problem 435.
Triangle, Incircle, Inradius, Incenter, Congruent circles, tangent,
Measurement. 

Proposed Problem 419.
Triangle, Cevian, Incircle, Excircle, Inradius, Exradius 

Proposed Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius. 

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence. 

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors. 

Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points. 

Sangaku Geometry Theorem: Cyclic Quadrilateral.
Incenters, Incircles, Inradii, Rectangle. 

Sangaku Problem (An Old Japanese Theorem).
Incenters, Incircles, Inradii, Carnot's theorem. 

Equal Incircles Theorem: Triangles,
cevians, circles. 

Adams' Circle
Theorem
Concentric to the Incircle. 

Spieker Center
Incenter of the medial triangle. 

Heron's Formula.
Key facts and
a purely geometric
stepbystep proof.
Incenter, Incircle, Excenter.


Semiperimeter and incircle of a triangle. 

Semiperimeter, incircle and excircles of a triangle.


Gergonne Point Theorem.
Incenter, Incircle, Concurrency. Interactive proof with animation.
Key concept: Ceva's Theorem.


The Bevan Point The
circumcenter of the excentral triangle.
Illustration with animation.


Interactive Gergonne Line and Nobbs Points.
Dynamic Geometry.
StepbyStep construction, Manipulation, and animation.
Incenter and the points of contact of the incircle. 

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

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean,
hypotenuse, cathetus (legs), semiperimeter, altitude, median,
similar shapes areas, centers, orthocenter, incenter,
incircle, centroid, circumcenter, radius, inradius. 

Feuerbach
Point Facts
Incenter, Incircle, Nine point circle, Circumcircle. 

Feuerbach
Theorem, Acute Triangle illustration


Feuerbach
Theorem, Obtuse Triangle illustration


Feuerbach
Theorem, Right Triangle illustration


Feuerbach Theorem
One of the most striking theorems in triangle geometry. 

Proposed Problem 279 Incircle.
Tangent Circles, Common External Tangent, Chords, Inradius. 

Proposed Problem 275.
Right Triangle, Incenter, Circumcircle, Sagitta, Inradius. 

Proposed Problem 260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances,
Squares.


Proposed Problem 259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances,
Squares.


Proposed Problem 258 Incircle.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.


Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

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