Plane Geometry: Intersection of a Line with a Circle, Theorems and Problems

Intersection of a Line with a Circle, Theorems and Problems: Table of Content

Seven Circles Theorem
Tangent circles, Intersection of a Line with a Circle.

Geometry Problem 795
Intersecting Circles, Common Chord, Midpoint, Tangent, Secant Line, Perpendicular, 90 Degrees.

Geometry Problem 788
Intersecting Circles, Secant Line, Midpoint, Cyclic Quadrilateral.

Geometry Problem 773
Intersecting Circles, Midpoint, Secant line, Bisection.

Geometry Problem 767
Equilateral Triangle, Circle tangent to a side, Tangent line, Measurement, Secant.

Geometry Problem 738.
Intersecting Circles, External Common Tangent, Common Chord, Secant, Circumcircle, Cyclic Quadrilateral, Concyclic Points.

Problem 575.
Cyclic quadrilateral, Angle bisector, Measurement, Intersection of a Line with a Circle.

Problem 574.
Circle, Chord, Secant, Angle Bisector, Perpendicular, Intersection of a Line with a Circle.

Problem 573.
Cyclic quadrilateral, Angle bisector, Perpendicular, Intersection of a Line with a Circle.

Problem 571.
Circle, Diameter, Chord, Perpendicular, Measurement, Intersection of a Line with a Circle.

Problem 568.
Triangle, Excircles, Tangency Point, Congruence, Intersection of a Line with a Circle.

Problem 567.
Right triangle, Incircle, Excircle, Collinear tangency points, Intersection of a Line with a Circle.

Problem 565.
Triangle, Isogonal lines, Angles, Congruence, Concyclic Points, Intersection of a Line with a Circle.

Problem 564.
Complete Quadrilateral, Incenter, Excenter, Concyclic Points, Incircle, Excircle, Intersection of a Line with a Circle.

Problem 548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points, Similarity, Intersection of a Line with a Circle.

Problem 547.
Triangle, Transversal, Four Circumcircles, Concurrency, Intersection of a Line with a Circle.

Problem 538.
Triangle, Perpendicular Bisector, Circumcircle, Midpoint, Intersection of a Line with a Circle.

Problem 532.
Triangle, Circumcircle, Equal Angles, Perpendicular, Area, Intersection of a Line with a Circle.

Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Perpendicular, Congruence, Intersection of a Line with a Circle.

Problem 529.
Right Trapezoid, Circle, Diameter, Intersection of a Line with a Circle.

Problem 527.
Circle, Tangent, Secant, Chord, Midpoint, Measurement, Intersection of a Line with a Circle.

Problem 526.
Equilateral Triangle, Circumcircle, Chord, Measurement, Intersection of a Line with a Circle.

Problem 525.
Circles, Diameter, Tangent, Radius, Congruence, Measurement, Intersection of a Line with a Circle.

Problem 522.
Right Triangle, Circle, Diameter, Tangent, Intersection of a Line with a Circle.

Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure, Intersection of a Line with a Circle.

Problem 493.
Right Triangle, Circumcircle, Perpendicular, Chord, Intersection of a Line with a Circle.

Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel, Intersection of a Line with a Circle.

Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle, Intersection of a Line with a Circle.

Problem 487.
Intersecting Circles, Area, Diameter, Parallel, 90 Degrees, Intersection of a Line with a Circle.

Problem 486.
Tangent circles, Chord, Arc, Midpoint, Collinearity, Congruence, Intersection of a Line with a Circle.

Problem 476.
Triangle, Circumcenter, Circumcircle, Angles, Intersection of a Line with a Circle.

Problem 475.
Tangent Circles, Secant, Tangent, Parallel, Intersection of a Line with a Circle.

Problem 474.
Parallelogram, Diagonal, Circle, Vertex, Intersection of a Line with a Circle.

Problem 468.
Circle, Chord, Midpoint, Congruence, Angle, Intersection of a Line with a Circle.

Proposed Problem 466.
Concentric Circles, Secant, Congruence, Measurement, Intersection of a Line with a Circle.

Proposed Problem 463.
Three Concentric Circles, Secant, Tangent, Triangle, Area, Intersection of a Line with a Circle.

Proposed Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement, Intersection of a Line with a Circle.

Proposed Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement, Intersection of a Line with a Circle.

Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear, Intersection of a Line with a Circle.

Proposed Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees, Intersection of a Line with a Circle.

Proposed Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius, Intersection of a Line with a Circle.

Proposed Problem 453.
Intersecting Circles, Tangent, Circular Segment, Congruence, Area, Intersection of a Line with a Circle.

Proposed Problem 452.
Triangle, Circle, Tangent, Proportional Segments, Intersection of a Line with a Circle.

Proposed Problem 444.
Internally Tangent circles, Secant line, Chords, Angles, Congruence, Intersection of a Line with a Circle.

Proposed Problem 443.
Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles, Intersection of a Line with a Circle.

Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Parallel lines, Intersection of a Line with a Circle.

Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Intersection of a Line with a Circle.

Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Intersection of a Line with a Circle.

Proposed Problem 417.
Tangent circles, Tangent lines, Angles, Intersection of a Line with a Circle.

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence, Intersection of a Line with a Circle.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear, Intersection of a Line with a Circle.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles, Intersection of a Line with a Circle.

Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent, Intersection of a Line with a Circle.

Proposed Problem 279.
Tangent Circles, Common External Tangent, Chords, Inradius, Intersection of a Line with a Circle.

Mascheroni Construction with compass alone. Midpoint of a segment.
Intersecting circles. Tangent circles, Intersection of a Line with a Circle.

Proposed Problem 190. Tangent circles, Tangent chord, Perpendicular, Distance, Intersection of a Line with a Circle.