Online Geometry

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

Incenter, Incircle, Index


Circle, Angle, Incenter, Isosceles triangle

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

Triangle, CIrcle, Incircle, Inradius

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

Triangle, Incircle, Excircle, Inradius, Exradius

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

Triangle, Incircle, Inradius, Tangent

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

Triangle, Incenter, Parallel to a side

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

Tiangle, Incenter, Angle

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

Triangle, Circumcenter, Incenter, Excenter, Collinear

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

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.

Gergonne Line

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

Interactive Geometry

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.

Elearning 279: Tangent circles

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

Sagitta Problem

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

Elearning 260: Problem about equilateral triangle

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

Elearning 259: Equilateral triangle, Incircle

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

Elearning 258: Equilateral triangle, Incircle

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

Elearning: Napoleon Theorem III

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

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Last updated: Mar 9, 2022