Online Geometry: Tangent Circles, Theorems and Problems

Tangent Circles, Theorems and Problems: Table of Content

Second Ajima-Malfatti Point
Interactive illustration.
Tangent circles.

First Ajima-Malfatti Point
Animated illustration.
Tangent circles.

Sawayama -Thebault's theorem
Tangent circles.

Apollonius' Problem for Three Circles Illustration with animation and sound.
Tangent circles

Seven Circles Theorem
Tangent circles.

Soddy Circles and Descartes Theorem.
Three tangent circles, Inscribed and Circumscribed Circles, Radii.

Arbelos, Theorems and Problems
Three tangent semicircles with collinear centers.
Index 

Geometry Problem 713.
Tangent Circles, Diameter, Chord, Tangent, Incenter, Incircle, Triangle.

Geometry Problem 708.
Circle, Tangent, Intersecting, Lune, Area, Diameter.

Geometry Problem 673.
Internally tangent circles, Chord, Tangent, Metric Relations.

Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean.

Geometry Problem 650.
Tangent Circles, Diameter, Radius, Chord, Perpendicular.

Geometry Problem 639
Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence.

Geometry Problem 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos.

Geometry Problem 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent.

Problem 635
Semicircle, Diameter, Perpendicular, Inscribed Circle, Radius.

Problem 572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles.

Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity.

Problem 490.
Tangent Circles, Arc, Radius, Circular Sector, Area.

Proposed Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement.

Proposed Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.

Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear.

Proposed Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius.

Proposed Problem 449.
Congruent Tangent Circles, Diameter, Sagitta, Arc, Perpendicular, Chord.

Proposed Problem 445.
Three Tangent Circles, Tangency Points, Circumradius.

Proposed Problem 444.
Internally Tangent circles, Secant line, Chords, Angles, Congruence.

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

Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Parallel lines.

Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

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

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

Proposed Problem 417.
Tangent circles, Tangent lines, Angles.

Proposed Problem 403.
Circular sector, 90 degrees, Circle, Semicircle, Area.

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Proposed Problem 336.
Two equal circles, a Common Tangent and a Square.

Proposed Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent.

Proposed Problem 315.
Three Tangent circles, Common external tangent line, Geometric Mean.

Proposed Problem 314.
Tangent circles, Common external tangent line, Geometric Mean.

Proposed Problem 311.
Circle Inscribed in a Semicircle, Chord, Diameter.
Tangent circles.

Proposed Problem 310.
Circle Inscribed in a Semicircle, 45 Degrees Angle.
Tangent circles.

Proposed Problem 295.
Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Perpendicular.
Tangent circles.

Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent.

Geometry Expressions.
Tangent circles.

Proposed Problem 289: Tangent circles, Radius, Perpendicular, Tangent.

Proposed Problem 288: Tangent circles, Harmonic Mean, Radius, Diameter.

Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent.

Proposed Problem 289.
Tangent circles, Radius, Perpendicular, Tangent.

Proposed Problem 285.
Circular Sector 90 degrees, Semicircles, Tangent circles, Radius.

Proposed Problem 284.
Circular Sector 90 degrees, Semicircles, Tangent circles, Radius.

Proposed Problem 283.
Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius.
Tangent circles.

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

Proposed Problem 278.
Tangent Circles, Common External Tangent, Chord.

Proposed Problem 277.
Tangent Circles, Common External Tangent.

Proposed Problem 271.
Tangent Circles, the Cube of the Common external tangent.

Proposed Problem 270.
Tangent Circles, Common external tangent, Fractional exponents.

Mascheroni Construction with compass alone. Midpoint of a segment.
Intersecting circles. Tangent circles.

Proposed Problem 213. Triangle, Incircle, Inradius, Semicircles, Common Tangents.  

Proposed Problem 190. Tangent circles, Tangent chord, Perpendicular, Distance.

Proposed Problem 180. Externally Tangent circles, Common External Tangents, Areas.

Proposed Problem 145. Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters. Tangent circles. 

Proposed Problem 143. Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii. Tangent circles. 

Proposed Problem 100. Circle Area, Archimedes' Book of Lemmas. Tangent circles.

Proposed Problem 99: Circle Area, General Extension to Pythagoras' Theorem.

Circumcircles or circumscribed circle
Proposed Problem 94. Similar Triangles, Circumcircles, Circumradii. Tangent circles.

Circumcircles or circumscribed circle
Proposed Problem 93. Similar Triangles, Circumcircles, Parallelogram. Tangent circles.

Circumcircles or circumscribed circle
Proposed Problem 92. Similar Triangles, Circumcircles, Circumradii, Parallel.

Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.
Tangent circles.

Three Tangent Circles Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.

Sangaku Geometry Theorem: Three circles and a tangent line.

Arbelos, Inscribed Circle and Concyclic Points Cyclic Quadrilateral.
Tangent circles.

Proposed Problem 57: Angle bisector, circles Cyclic Quadrilateral.
Tangent circles.

Proposed Problem 56: Angle bisector, circles Parallel Lines.
Tangent circles.

Proposed Problem 55: Angle bisector, circles Cyclic Quadrilateral.
Tangent circles.

Proposed Problem 54: Angle bisector, circles Midpoint of arc.
Tangent circles.

Proposed Problem 53: Angle bisector, circles.
Tangent circles.

Feuerbach Point Facts
Tangent circles. 

Feuerbach Theorem, Acute Triangle illustration
Tangent circles. 

Feuerbach Theorem, Obtuse Triangle illustration
Tangent circles. 

Sangaku Proposed Problem 41. "Mickey Mouse."
Three circles, tangents, radii.

Archimedes' Book of Lemmas
Tangent circles. 

An Isoperimetric theorem
Tangent circles.

The Descartes Circle Theorem
Tangent circles.