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 step-by-step 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.
Step-by-Step construction, Manipulation, and animation.
Incenter and the points of contact of the incircle.

Triangle: Incircle, Perpendicular, Angle Bisector. Dynamic Geometry.
Step-by-Step 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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