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Angle Bisector, Theorems and Problems - Table of Content 1
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![Angle Bisector Index](angle_bisector_index_17.jpg) |
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![Euclid's Elements 23 definitions](euclid_elements_definition_170.jpg) |
Euclid's Elements
Book I, 23 Definitions. One-page visual illustration. Angles and more.
Euclid's Elements Book.
Index. |
![Bisect an angle](euclid_elements_book_i_9_17.jpg) |
Book I, Proposition 9: Bisect a given angle.
Construction of angle bisector
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![Incenter, Incircle, Index](../center/incenter_incircle_17.jpg) |
Incenter. Index.
Angle bisectors
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![Angle Bisector Theorem](euclid_elements_vi_3_bisect.jpg) |
Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem |
![Isogonal Lines](../math_geometry_online_courses/isogonal-lines-conjugate-theorems-problems-index-1.jpg) |
Isogonal Lines.
Theorems and Problems. |
![Dynamic Geometry: Incenter and Incircle of a Triangle. HTML5 Animation for Tablets (iPad, Nexus..)](../center/incenter-incircle-geogebra-html5-animation-tablet-mobile-ipad-nexus-1.jpg) |
GeoGebra, Dynamic Geometry: Incenter and Incircle
of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..) |
![Morley's Theorem](morley_theorem_170.jpg) |
Animated
illustration of the celebrated Morley's angle trisector theorem |
![](morley_triangle_center_17.jpg) |
Morley's Triangle & Center: Trisection of angles. |
![](../problem/blanchet_theorem_170.jpg) |
Blanchet Theorem.
Altitude, Angle Bisector.
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![](isogonic_jacobi_theorem_1.jpg) |
Isogonic-Jacobi
Theorem: Using TracenPoche Dynamic
Geometry Software.
Isogonal conjugate line,
reflecting line on the angle bisector |
![Interactive Geometry](triangle_incircle_perpendic.jpg) |
Triangle: Incircle, Perpendicular, Angle Bisector.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
![](../heron/heron__proof_170x100.jpg) |
Heron's Formula.
Key facts and
a purely geometric
step-by-step proof.
Geometry help: Key Facts: Angle bisector.
Preliminary propositions |
![Geometry Problem 1571](../school-college/6/p1571-pythagorean-triangle-triple-7-24-25-prove-angle-74-degrees-tutoring-1.jpg) |
Geometry Problem 1571:
Prove that the intermediate angle in a Pythagorean Triple 7-24-25 measures 74 degrees. |
![Geometry Problem 1564](../school-college/6/p1564-find-area-quadrilateral-in-right-triangle-abc-with-altitude-bisectors-midpoint-tutoring-1.jpg) |
Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
![Geometry Problem 1563](../school-college/6/p1563-midpoint-mysteries-proving-perpendicularity-in-right-triangle-abc-altitude-bisectors-1.jpg) |
Geometry Problem 1563:
Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
![Geometry Problem 1562](../school-college/6/p1562-right-angled-triangle-bisector-midpoint-collinear-points-proof-1.jpg) |
Geometry Problem 1562:
Proof of Collinearity in a Right-angled Triangle involving the Altitude, Angle bisectors, and Midpoint. |
![Geometry Problem 1553](../school-college/6/p1553-triangle-abc-angle-bisectors-calculate-circumradius-1.jpg) |
Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors |
![Geometry Problem 1550](../school-college/6/p1550-right-triangle-angle-based-segment-length-calculation-isosceles-congruence-1.jpg) |
Geometry Problem 1550: Solving for Segment BD: An Angle Puzzle in Right Triangle ABC: A High School Level Investigation |
![Geometry Problem 1549](../school-college/6/p1549-triangle-incircle-tangent-inscribed-circle-angle-calculation-1.jpg) |
Geometry Problem 1549: Unraveling the Geometric Mystery: Calculating Angle
BGE with the Incircle and Tangent in Triangle ABC |
![Geometry Problem 1547](../school-college/6/p1547_circle_radius_4_tangents_AB_AC_points_of_tangency_distance_calculation_from_B_to_AC-1.jpg) |
Geometry Problem 1547: Tangents' Dance: Exploring B-to-AC Distance in a
Circle's Grasp |
![Geometry Problem 1542](../school-college/6/p1542-right-triangle-square-circumscribed-inscribed-circle-hypotenuse-segment-length-angle-bisector-1.jpg) |
Geometry Problem 1542: Unraveling a Geometric Puzzle with a Circumscribed
Right Triangle and Square to the Same Circle for School and College. |
![Geometry Problem 1526](../school-college/6/p1526-parallelogram-intersecting-bisectors-distance-congruence-1.jpg) |
Geometry
Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures.
. |
![Geometry Problem 1524](../school-college/6/p1524-parallelogram-angle-bisector-intersect-distance-1.jpg) |
Geometry
Problem 1524 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors. |
![Geometry Problem 1518](../school-college/6/p1518-solve-number-of-sides-equiangular-polygon-angle-bisector-interior-point-1.jpg) |
Geometry
Problem 1518 and a Thematic Poem.
Boost Your Geometry Skills: Solve for the Number of Sides in an Equiangular Polygon with an Interior Point and Bisected Angle. |
![Geometry Problem 1505](../school-college/6/p1505-three-parallel-rays-angles-corresponding-alternate-consecutive-bisector-1.jpg) |
Geometry
Problem 1505.
Parallel Rays, Angles, and Bisector, Corresponding, Alternate, Conjugate. |
![Geometry Problem 1502](../school-college/6/p1502-rigth-triangle-incircles-measurement-inradius-square-quadrilateral-1.jpg) |
Geometry
Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral. |
![Geometry Problem 1491](../school-college/5/p1491-cyclic-quadrilateral-diagonal-incircle-angle-measurement-1.gif) |
Geometry
Problem 1491.
Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement. |
![Geometry Problem 1490](../school-college/5/p1490-triangle-cevian-incircle-tangent-measurement-1.gif) |
Geometry
Problem 1490.
Triangle, Cevian, Incircle, Tangent, Measurement. |
![Geometry Problem 1489](../school-college/5/p1489-right-triangle-angle-bisector-perpendicular-measurement-1.gif) |
Geometry
Problem 1489.
Right Triangle, Angle Bisectors, Perpendicular, Measurement. |
![Geometry Problem 1488](../school-college/5/p1488-right-triangle-altitude-angle-bisector-measurement-1.gif) |
Geometry
Problem 1488.
Right Triangle, Altitude, Incircle, Tangent, Measurement. |
![Geometry Problem 1487](../school-college/5/p1487-right-triangle-altitude-angle-bisector-measurement-1.gif) |
Geometry
Problem 1487.
Right Triangle, Altitude, Incircle, Tangent, Measurement. |
![Dynamic Geometry 1480](../school-college/5/p1480-cyclic-polygon-triangulation-sum-inradii-invariant-geogebra-ipad-1.jpg) |
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 1479](../school-college/5/p1479-triangle-circumcircle-angle-perpendicular-bisector-parallel-concyclic-geogebra-ipad-1.jpg) |
Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector,
Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra,
iPad. |
![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 1418](../school-college/5/p1418-triangle-incenter-parallel-angle-circle-tangent-1.jpg) |
Geometry Problem 1418. Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle. |
![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 1388 Circle, Triangle](../school-college/4/p1385-triangle-circumcircle-orthocenter-bisector-collinear-1.jpg) |
Geometry Problem 1385. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points. |
![Problem 1388 Circle, Triangle](../school-college/4/p1384-triangle-circumcircle-orthocenter-bisector-90-degree-1.jpg) |
Geometry Problem 1384. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree. |
![Geometry problem 1366](../school-college/4/p1366-square-perpendicular-angle-bisector-concylic-1.jpg) |
Geometry Problem 1366.
Square, Angle Bisector, Perpendicular, Concyclic Points, Circle, Sketch, iPad Apps. |
![Geometry problem 1364](../school-college/4/p1364-square-inscribed-circle-chord-pieces-area-1.jpg) |
Geometry Problem 1364.
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps. |
![Geometry problem 1363](../school-college/4/p1363-square-perpendicular-angle-bisector-45-degree-1.jpg) |
Geometry Problem 1363.
Square, Angle Bisector, Perpendicular, 45 Degrees, Angle, Sketch, iPad Apps. |
![Geometry problem 1347](../school-college/4/p1347-equilateral-triangle-bisector-circle-tangent-tutoring-1.jpg) |
Geometry Problem 1347. Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle. |
![Geometry problem 1341](../school-college/4/p1341-isosceles-triangle-80-20-80-bisector-circumcenter-1.jpg) |
Problem 1341.
Geometry Problem 1341: Isosceles Triangle, 80-20-80 Degrees, Circumcenter, Angle Bisector.
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![Geometry problem 1326](../school-college/4/p1326-triangle-cevian-incircle-angle-270-degree-1.jpg) |
Geometry Problem 1326.
Triangle, Cevian, Incenters, Sum of Angles, 270 Degrees. |
![Geometry problem 1324](../school-college/4/p1324-quadrilateral-isosceles-45-degree-angle-1.jpg) |
Geometry Problem 1324.
Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence. |
![Geometry problem 1322](../school-college/4/p1322-triangle-bisector-circle-sum-angle-1.jpg) |
Geometry Problem 1322.
Triangle, Angle Bisector, Circumcircle, Chord, Secant, Sum of two Angles. |
![Geometry problem 1307](../school-college/4/p1307-triangle-incenter-parallel-measurement-1.jpg) |
Geometry Problem 1307.
Triangle, Incenter, Parallel line, Sides, Measurement. |
![Geometry problem 1305](../school-college/4/p1305-triangle-angle-bisector-circumcircle-perpendicular-area-1.jpg) |
Geometry Problem 1305.
Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area. |
![Geometry problem 1304](../school-college/4/p1304-triangle-120-degrees-angle-bisector-1.jpg) |
Geometry Problem 1304.
Triangle, 120 Degrees, Angle Bisector, Measurement. |
![Geometry problem 1303](../school-college/4/p1303-triangle-60-degrees-angle-bisector-1.jpg) |
Geometry Problem 1303.
Triangle, 60 Degrees, Angle Bisector, Measurement. |
![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 1290](../school-college/3/p1290-triangle-median-angle-bisector-parallel-1.jpg) |
Geometry Problem 1290.
Triangle, Internal Angle Bisector, Median, Parallel, Measurement, Metric Relations. |
![Geometry problem 1274](../school-college/3/p1274-isosceles-triangle-80-20-80-measurement-1.jpg) |
Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement. |
![Geometry problem 1271](../school-college/3/p1271-triangle-incircle-excircle-concyclic-tutoring-1.jpg) |
Geometry Problem 1271.
Triangle, Incircle, Incenter, Excircle, Excenter, Escribed Circle, Tangency Points, Six Concyclic Points. |
![Geometry problem 1270](../school-college/3/p1270-triangle-excircle-bisector-90-degree-1.jpg) |
Geometry Problem 1270.
Triangle, Excircle, Excenter, Escribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1269](../school-college/3/p1269-triangle-incircle-bisector-90-degree-1.jpg) |
Geometry Problem 1269.
Triangle, Incircle, Incenter, Inscribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1268](../school-college/3/p1268-triangle-circle-angle-bisector-concyclic-1.jpg) |
Geometry Problem 1268.
Triangle, Exterior Angle Bisector, Circumcircle, Circle, Chord, Parallel, Concyclic Points, Cyclic Quadrilateral. |
![Geometry problem 1266](../school-college/3/p1266-triangle-excircle-90-degree-bisector-1.jpg) |
Geometry Problem 1266.
Triangle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1265](../school-college/3/p1265-triangle-incircle-90-degree-bisector-1.jpg) |
Geometry Problem 1265.
Triangle, Incircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1264](../school-college/3/p1264-triangle-exterior-angle-bisector-90-degree-concurrent
-1.jpg) |
Geometry Problem 1264.
Triangle, Exterior Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1260](../school-college/3/p1260-triangle-angle-bisector-90-degree-concurrent-1.jpg) |
Geometry Problem 1260.
Triangle, Internal Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1256](../school-college/3/p1256-parallelogram-angle-bisector-triangle-1.jpg) |
Geometry Problem 1256.
Parallelogram, Angle Bisector, Measurement. |
![Geometry problem 1249](../school-college/3/p1249-cyclic-quadrilateral-bisector-triangle-area-1.jpg) |
Geometry Problem 1249.
Cyclic Quadrilateral, Circle, Triangle, Circumcircle, Angle Bisector, Parallel Lines, Area. |
![Geometry problem 1243](../school-college/3/p1243-quadrilateral-angle-bisector-diagonal-1.jpg) |
Geometry Problem 1243.
Quadrilateral, Four Exterior Angle Bisectors, Semi-sum, Angles. Mobile Apps. |
![Geometry problem 1242](../school-college/3/p1242-quadrilateral-angle-bisector-collinearity-1.jpg) |
Geometry Problem 1242.
Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines. Mobile Apps. |
![Geometry problem 1241](../school-college/3/p1241-quadrilateral-exterior-angle-bisector-circle-cyclic-1.jpg) |
Geometry Problem 1241.
Quadrilateral, Four Exterior Angle Bisectors, Cyclic Quadrilateral, Circle. Mobile Apps. |
![Geometry problem 1231](../school-college/3/p1231-triangle-orthocenter-circumcenter-incenter-bisector-1.jpg) |
Geometry Problem 1231
Triangle, Orthocenter, Incenter, Circumcenter, Angle Bisector, Center, Circle. |
![Geometry problem 1227](../school-college/3/p1227-triangle-circle-bisector-concyclic-cyclic-1.jpg) |
Geometry Problem 1227
Triangle, Circumcircle, Angle Bisector, Concyclic Points, Cyclic Quadrilateral. |
![Geometry problem 1225](../school-college/3/p1225-equilateral-triangle-bisector-circle-congruence-1.jpg) |
Geometry Problem 1225
Equilateral Triangle, Circumcircle, Angle Bisector, Congruence. |
![Geometry problem 1217](../school-college/3/p1217-triangle-angle-bisector-cyclic-quadrilateral-class-1.jpg) |
Geometry Problem 1217
Triangle, Circle, Excenter, Incenter, Angle Bisector, Cyclic Quadrilateral, Circumcircle, Tangent Line. |
![Geometry problem 1214](../school-college/3/p1214-triangle-3-angle-bisector-class-1.jpg) |
Geometry Problem 1214
Triangle, Three Angle Bisectors, Proportions. |
![Geometry problem 1211](../school-college/3/p1211-right-triangle-altitude-bisector-45-degrees-class-1.jpg) |
Geometry Problem 1211
Right Triangle, Altitude, Angle Bisector, 45 Degrees. |
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