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Geometry: Tangent Circles, Theorems and Problems,
Page 1
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Tangent Circles, Table of Content
1/8
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![Tangent Circles Index](tangent_circles_index_17.jpg) |
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![](../center/ajima_malfatti_170_2.jpg) |
Second Ajima-Malfatti Point
Interactive illustration.
Tangent circles. |
![](../center/ajima_malfatti_170.jpg) |
First Ajima-Malfatti Point
Animated illustration.
Tangent circles. |
![](../problem/sawa_thebault_theorem_170.jpg) |
Sawayama -Thebault's
theorem
Tangent circles. |
![](apollonius_problem_circle_1.jpg) |
Apollonius' Problem for Three Circles
Illustration with animation and sound.
Tangent circles |
![](seven_circle_theorem_170.jpg)
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Seven Circles Theorem
Tangent circles. |
![Soddy Circles and Descartes Theorem](../geometry/soddy_descartes_circle_17.jpg) |
Soddy Circles and Descartes Theorem.
Three tangent circles,
Inscribed and Circumscribed Circles, Radii. |
![Arbelos, Theorems and Problems Index](../math_geometry_online_courses/arbelos_index_1.jpg)
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Arbelos, Theorems and Problems
Three tangent semicircles with collinear
centers.
Index |
![Euclidean Egg with 8 Arcs in 5 Steps, Step-by-Step Construction. HTML5 Animation](../geogebra/euclidean-egg-8-arcs-step-construction-html5-animation-ipad-tablet-1.jpg) |
GeoGebra,
Dynamic Geometry, Euclidean Egg with 8 Arcs in 5 Steps, Step-by-Step Construction
HTML5 Animation for Tablets (iPad, Nexus) |
![Euclidean Egg, Step-by-Step Construction. HTML5 Animation](../geogebra/euclidean-egg-step-construction-html5-animation-ipad-tablet-1.jpg) |
GeoGebra,
Dynamic Geometry, Euclidean Egg, Step-by-Step Construction
HTML5 Animation for Tablets (iPad, Nexus) |
![Art: Tangent Circles and Delaunay](../computational_geometry/delaunay-triangulation/tangent-circles-kids-art-delaunay-ipad-apps-software-1.jpg) |
Geometric Art:
Tangent Circles, Delaunay Triangulation, iPad,
iPhone App: Trimaginator. |
![Geometry Problem 1534](../school-college/6/p1534-tangent-circle-common-external-tangent-angle-brainteaser-1.jpg) |
Geometry
Problem 1534: High School Brainteaser: Tangent Circles, Common External Tangent, and Angle Conundrums!.
. |
![Problem 1435](../school-college/5/p1435-circle-diameter-tangent-parallelogram-1.jpg) |
Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points,
Poster, Typography, iPad Apps. |
![Problem 1434](../school-college/5/p1434-equilateral-triangle-tangent-circles-line-1.jpg) |
Geometry Problem 1434.
Equilateral Triangle, Tangent Circles, Tangent Lines, Arithmetic Mean, Measurement,
Poster, Typography, iPad Apps. |
![Problem 1433](../school-college/5/p1433-tangent-circles-line-midpoint-1.jpg) |
Geometry Problem 1433.
Tangent Circles, Diameter, Perpendicular, Midpoint, Measurement,
Poster Typography, iPad Apps. |
![Problem 1432](../school-college/5/p1432-tangent-circles-proportion-similarity-ipad-apps-1.jpg) |
Geometry Problem 1432.
Tangent Circles, Secant, Tangent Lines, Proportionality, Similarity,
Poster Typography, iPad. |
![Problem 1431](../school-college/5/p1431-apollonius-llc-triangle-circumcircle-tangent-congruent-angle-1.jpg) |
Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping. |
![Problem 1427](../school-college/5/p1427-square-circle-tangent-radius-1.jpg) |
Geometry Problem 1427. Circle inscribed in a square, Arc, Tangent Line, Tangent Circles, Radii. |
![Problem 1421](../school-college/5/p1421-right-triangle-incircle-excircle-measurement-1.jpg) |
Geometry Problem 1421. Right Triangle, Incircle, Excircle, Tangent Lines, Measurement. |
![Problem 1420](../school-college/5/p1420-circle-area-regular-hexagon-tangent-1.jpg) |
Geometry Problem 1420. Regular Hexagon, Inscribed Circle, Area, Tangent
Circles, Tangent Line. |
![Problem 1419](../school-college/5/p1419-triangle-incenter-inradius-circumcircle-distance-sketch-ipad-1.jpg) |
Geometry Problem 1419. Triangle, Altitude, Circumcircle, Incenter, Inradius, Perpendicular, Angle Bisector, Midpoint. |
![Problem 1417](../school-college/5/p1417-triangle-incenter-circumcircle-tangent-cevian-bisector-perpendicular-1.jpg) |
Geometry Problem 1417. Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector,
Tangent Lines, Tangent Circles. |
![Problem 1402](../school-college/5/p1402-triangle-three-tangent-circles-diameter-collinearity-tutor-1.jpg) |
Geometry Problem 1402. Triangle, Three Tangent Circles, Parallel Diameter, Collinear Points. |
![Geometry problem 1362](../school-college/4/p1362-equilateral-triangle-inscribed-circle-lunula-area-1.jpg) |
Geometry Problem 1362.
Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps. |
![Geometry problem 1353](../school-college/4/p1353-tangent-circle-congruence-30-degrees-1.jpg) |
Geometry Problem 1353. Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees. |
![Geometry problem 1314](../school-college/4/p1314-equilateral-triangle-incircle-tangent-congruence-1.jpg) |
Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence. |
![Geometry problem 1301](../school-college/4/p1301-arbelos-incircle-square-midpoint-1.jpg) |
Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. |
![Geometry problem 1300](../school-college/3/p1300-arbelos-incircle-tangent-bisector-concurrency-1.jpg) |
Geometry Problem 1300.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Perpendicular, Concurrent Lines. |
![Geometry problem 1298](../school-college/3/p1298-arbelos-incircle-angle-bisector-perpendicular-midpoint-1.jpg) |
Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint. |
![Geometry problem 1297](../school-college/3/p1297-arbelos-incircle-tangent-angle-bisector-1.jpg) |
Geometry Problem 1297.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector. |
![Geometry problem 1277](../school-college/3/p1277-equilateral-triangle-externally-tangent-circle-tutoring-1.jpg) |
Geometry Problem 1277.
Equilateral Triangle, Circumcircle, Externally Tangent Circles, Tangent Line, Measurement. |
![Geometry problem 1276](../school-college/3/p1276-equilateral-triangle-internally-tangent-circle-tutoring-1.jpg) |
Geometry Problem 1276.
Equilateral Triangle, Circumcircle, Internally Tangent Circles, Tangent Line, Measurement. |
![Geometry problem 1229](../school-college/3/p1229-three-tangent-circles-line-3-4-5-triangle-1.jpg) |
Geometry Problem 1229
Three Tangent Circles, Midpoint, Common Tangent Line, 3-4-5 Right Triangle. |
![Geometry problem 1228](../school-college/3/p1228-three-tangent-circles-line-square-1.jpg) |
Geometry Problem 1228
Three Tangent Circles, Midpoint, Major Arc, Common Tangent Line, Square. |
![Geometry problem 1216](../school-college/3/p1216-3-circles-90-degrees-tangent-collinearity-class-1.jpg) |
Geometry Problem 1216
Circle, 90 Degrees, Tangent, Common Chord, Collinearity. |
![Geometry problem 1168](../school-college/2/p1168-arbelos-construction-inscribed-circle-triangle-proof-tutor-1.jpg) |
Geometry Problem 1168
Construction of the Inscribed Circle of the Arbelos, Semicircles, Diameter, Circle, Triangle, Circumcircle, Tangent. |
![Geometry problem 1158](../school-college/2/p1158-four-tangent-circles-chord-metric-relations-1.jpg) |
Geometry Problem 1158.
Four Tangent Circles, Tangent Chord, Radius, Metric Relations. |
![Geometry problem 1157](../school-college/2/p1157-four-tangent-circles-90-degrees-metric-relations-1.jpg) |
Geometry Problem 1157.
Four Circles, Mutually Tangent, 90 Degrees, Radius, Metric Relations. |
![Geometry problem 1154](p1154_sangaku_circles_tangent_line_art_02_1.jpg) |
Geometry Problem 1154. Sangaku Three circles and a tangent line. |
![Geometry problem 1148](../school-college/2/p1148-dynamic-right-triangle-circle-tangent-radius-ipad-animation-1.jpg) |
Dynamic Geometry Problem 1148
Static Geometry Problem 1148.
Right Triangle, Circle, Incircle, Circumcircle, Tangent, Radius. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). |
![Geometry problem 1143](../school-college/2/p1143-brain-geometry-triangle-circle-reflection-tangent-1.jpg) |
Geometry Problem 1143.
Triangle, Circumcircle, Tangent Line, Reflection of a Point over a Line, Tangent Circles, Collinear Points. |
![Geometry problem 1137](../school-college/2/p1137-triangle-orthocenter-circle-midpoint-collinear-1.jpg) |
Geometry Problem 1137.
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint, Arc, Collinear Points, Tangent Circles. |
![Geometry problem 1134](../school-college/2/p1134-circle-tangent-circumcenter-circumcircle-triangle-1.jpg) |
Geometry Problem 1134.
Tangent Circles, Tangent Line, Triangle, Circumcircle, Circumcenter. |
![Geometry Problem 1096](../school-college/1/p1096-four-tangent-circles-common-tangent-chord-radius-math-1.jpg) |
Geometry Problem
1096.
Tangent Circles, Common Tangent, Chord, Radius, Center. |
![Geometry Problem 1095](../school-college/1/p1095-tangent-circles-common-tangent-radius-geometric-mean-math-1.jpg) |
Geometry Problem
1095.
Externally Tangent Circles, Common Tangent, Radius, Metric Relations. |
![Geometry Problem 1094](../school-college/1/p1094-tangent-circles-chord-sagitta-radius-math-1.jpg) |
Geometry Problem
1094.
Tangent Circles, Tangent Chord, Radius, Sagitta of Arc. |
![Geometry Problem 1093](../school-college/1/p1093-square-circle-tangent-radius-side-sangaku-japanese-math-1.jpg) |
Geometry Problem
1093.
Square, Circle, Tangent, Radius, Side, Sangaku, Japanese Geometry Problem. |
![Geometry Problem 1087](../school-college/1/p1087-tangent-circle-angle-15-degrees-tutoring-math-1.jpg) |
Geometry Problem
1087.
Tangent Circles, Parallel, 15 Degrees, Angle. |
![Geometry Problem 1081](../school-college/1/p1081-equilateral-triangle-circle-tangent-radius-sangaku-class-math-1.jpg) |
Geometry Problem
1081.
Equilateral Triangle, Inscribed Circle, Inradius, Tangent Circles, Radius, Tangent Line, Sangaku Japanese Problem. |
![Geometry Problem 1077](../school-college/1/p1077-equal-tangent-circles-area-sector-sangaku-sacred-geometry-math-1.jpg) |
Geometry Problem
1077.
Chain of Equal Tangent Circles, Circular Sector, Area, Sangaku, Sacred Geometry. |
![Geometry Problem 1071](../school-college/1/p1071-arbelo-circle-semicircle-perpendicular-tangent-midpoint-problem-solving-tutor-1.jpg) |
Geometry Problem
1071.
Arbelos, Semicircles, Diameter, Circle, Perpendicular, Common Tangent, Parallel, Collinear Points, 90 Degrees,
Midpoint. |
![Geometry Problem 1048](../school-college/1/p1048-tangent-circles-common-tangent-chord-metric-relations-math-1.jpg) |
Geometry Problem
1048.
Circles, Tangent, Perpendicular, Diameter, Angle Bisector. |
![Geometry Problem 1009](../school-college/1/p1009-tangent-circles-common-external-internal-arithmetic-mean-math-1.jpg) |
Geometry Problem
1009.
Tangent Circles, Common External Tangent, Common Internal Tangent, Arithmetic Mean. |
![Geometry Problem 1008](../school-college/1/p1008-three-equal-tangent-circles-sum-lines-math-1.jpg) |
Geometry Problem
1008.
Three Equal Tangent Circles, Sum of Tangent Lines, Tangency Points. |
![Geometry Problem 1006](../school-college/1/p1006-tangent-circles-common-external-metric-relations-math-1.jpg) |
Geometry Problem
1006.
Tangent Circles, Common External Tangent, Bicentric Trapezoid, Incenter, Circumcenter. |
![Geometry Problem 989](../school-college/p989-semicircle-arbelo-perpendicular-tangent-rectangle-midpoint-arc-1.jpg) |
Geometry Problem 989.
Arbelos, Semicircles, Diameter, Perpendicular, 90 Degree, Common External Tangent, Rectangle, Midpoint of Arc. |
![Geometry Problem 987](../school-college/p987-triangle-circumcircle-incenter-parallel-circle-tangent-animation-ipad-1.jpg) |
Geometry Problem 987.
Triangle, Circumcircle, Incenter, Chord, Parallel, Circle, Tangent. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). |
![Geometry Problem 952](../school-college/p952-triangle-3-equal-circles-tangent-incenter-circumcenter-collinear-1.jpg) |
Geometry Problem 952.
Triangle, Incenter, Circumcenter, Three Equal Circles, Tangent Line, Tangent Circles, Collinear Points. |
![Problem 941](../school-college/p941-tangent-circle-secant-proportion-equal-angle-1.jpg) |
Geometry Problem 941.
Circles Tangent Externally, Tangent, Secant, Proportion, Angle. |
![Problem 936](../school-college/p936-semicircle-diameter-circle-tangent-radius-metric-relations-1.jpg) |
Geometry Problem 936.
Circle, Semicircle, Diameter, Tangent, Radius, Chord, Metric Relations.
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![Tangent Circles, Diameter, Perpendicular, Triangle, Area, Tangency Point](../school-college/p823-circle-triangle-area-perpendicular-tangent-diameter-1.jpg) |
Geometry Problem 823.
Tangent Circles, Diameter, Perpendicular, Chord, Secant, Triangle, Area, Tangency Point. |
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