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

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Triangle Centers.

Distances between Triangle Centers Index.

GeoGebra, Dynamic Geometry: Incenter and Incircle of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

Gergonne Points Index
Triangle Center

Nagel Points Index
Triangle Center

Right triangle, Altitude, Incircle
Right Triangle, Altitude to the Hypotenuse, Incircle, Incenter, Inradius, Angle Bisector, Theorems and Problems, Index.

Sawayama -Thebault's theorem
Incenter, Incircle, Circumcircle.

Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.

Geometry Problem 1584: Proving a Ratio Involving Incircle and Angle Bisector
Unveiling a Potentially Unexplored Geometric Relationshp.

Geometry Problem 1569: Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF.

Geometry Problem 1568: Concyclicity of Points B, D , H, J in a Triangle ABC with an Incircle and a Tangent Circle.

Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence

Geometry Problem 1549: Unraveling the Geometric Mystery: Calculating Angle BGE with the Incircle and Tangent in Triangle ABC

Geometry Problem 1546: Discover the Hidden Geometry: Calculate Area of Contact Triangle DEF in Triangle ABC

Geometry Problem 1545: Unlock the Geometric Mystery: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters!

Geometry Problem 1542: Unraveling a Geometric Puzzle with a Circumscribed Right Triangle and Square to the Same Circle for School and College.

Geometry Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular.

Geometry Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral.

Geometry Problem 1492.
Right Triangle, Altitude, Incenters, Angle, Measurement.

Geometry Problem 1491.
Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement.

Geometry Problem 1490.
Triangle, Cevian, Incircle, Tangent, Measurement.

Geometry Problem 1489.
Right Triangle, Angle Bisectors, Perpendicular, Measurement.

Geometry Problem 1488.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1487.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1486.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1484.
Right Triangle, Altitude, Incircles, Inradius, Measurement.

Dynamic Geometry 1481.
Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1480.
Japanese Theorem for Cyclic Polygon, Sangaku, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1471.
Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration.

Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus, Step-by-step Illustration.

Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration.

Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration.

Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points. Step-by-step Illustration using GeoGebra.

Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1458.
Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra.

Geometry Problem 1457.
Altitudes, Circles, Similarity, Product of the Inradii Lengths, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1455.
Nagel Point, Excircles, Incircle, Congruent Segments, iPad. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1452.
Japanese Theorem, Sangaku, Cyclic Quadrilateral, Incenter, Rectangle, Inradius. Step-by-step illustration using GeoGebra.

Geometry Problem 1443.
Triangle Area, Incenter, Circumcenter, 90 Degree, Perpendicular, One-third Area, Art, Poster, Typography, iPad Apps.

Geometry Problem 1438.
Triangle, Incenter, Centroid, Circumcenter, Parallel, 90 Degree, Art, Poster, Typography, iPad Apps.

Geometry Problem 1421.
Right Triangle, Incircle, Excircle, Tangent Lines, Measurement.

Geometry Problem 1419.
Triangle, Altitude, Circumcircle, Incenter, Inradius, Perpendicular, Angle Bisector, Midpoint.

Geometry Problem 1418.
Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle.

Geometry Problem 1417.
Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector, Tangent Lines, Tangent Circles.

Geometry Problem 1416.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Geometry Problem 1415.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Geometry Problem 1414.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Geometry Problem 1413.
Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle.

Geometry Problem 1412.
Right Triangle, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Geometry Problem 1411.
Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle.

Geometry Problem 1410.
Right Triangle, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Geometry Problem 1409.
Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity.

Geometry Problem 1408.
Right Triangle, Incircle, Excircle, Incenter, Midpoint, Tangency Point, Collinearity.

Geometry Problem 1407.
Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity.

Geometry Problem 1388.
Triangle 40-60-80 degree, Incenter, Congruence.

Geometry Problem 1350.
Triangle with three Intersecting Circles, Incircle, Collinear Points.

Geometry Problem 1349.
Three Squares, 90 Degrees, Perpendicular Lines, Diagonal. Math Infographic.

Geometry Problem 1348.
Three Concentric Circles, Equilateral Triangle, Perpendicular Bisector, Congruence.

Geometry Problem 1347.
Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle.

Geometry Problem 1346.
Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance.

Geometry Problem 1345.
Three Equilateral Triangles, Center, Area, Common Vertex.

Geometry Problem 1344, Bottema's Theorem: Triangle and Squares with Interactive Geometry Software.

Problem 1343.
Triangle, Excircles, Circle, Tangent, Tangency Points, Chord, Perpendicular, 90 Degrees, Collinearity. Machu Picchu in the background.

Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.

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