Geometry Problems: High School, College

Geometry Problems 601-700

 

Geometry Problems 601-700

Online education degree: Open geometry problems

Open Geometry Problems - Index

Cyclic quadrilateral, Incenter, Excenter

Geometry Problem 601
Cyclic Quadrilateral, Incenter, Excenter, Rectangle.

Triangle, Angle, Congruence

Geometry Problem 602
Triangle, Angles, 30 and 45 Degrees, Cevian, Congruence.

Parallelogram, Diagonals

Geometry Problem 603
Parallelogram, Diagonals, Congruence, Concurrency.

Parallelogram Area

Geometry Problem 604
Parallelograms, Triangle, Trapezoid, Area.

Square, Circle, Metric Relation

Geometry Problem 605
Circle, Square, Chord, Perpendicular, Circular Segment, Metric Relations.

Isosceles triangle

Geometry Problem 606
Isosceles Triangles, Perpendicular and Parallel Lines.

Intersecting Circles

Geometry Problem 607
Intersecting Circles, Triangles, Metric Relations, Measurement.

Square with Right triangles

Geometry Problem 608
Square with Right Triangles, Metric Relations, Congruence, Measurement.

Triangle, Perpendiculars, Collinearity

Geometry Problem 609
Triangle, Perpendiculars, 90 Degrees, Collinearity.

Intersecting Circles, 90 degrees

Geometry Problem 610
Intersecting Circles, Radius, Parallel, Common Tangent, Angle, 90 Degrees.

Triangle, Altitude, Collinearity

Geometry Problem 611
Altitude of a Triangle, Perpendicular, Collinear Points, Parallel.

Triangle, Altitude, Congruence

Geometry Problem 612
Altitude of a Triangle, Perpendicular, Congruence.

Triangle, Altitude, Collinearity

Geometry Problem 613
Altitude of a Triangle, Perpendicular, Collinear Points.

Parallelogram, Diagonal, Parallel

Geometry Problem 614
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Triangle, Square, Area

Geometry Problem 615
Right Triangle with a Square, Diagonals, Center, Area of Quadrilateral.

Parallelogram, Diagonal, Parallel

Geometry Problem 616
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Right triangle area

Geometry Problem 617
Right Triangle Area, Incircle, Incenter, Tangent, 90 Degrees.

Triangle area, 60 degrees

Geometry Problem 618
Triangle Area, 60 Degrees, Incircle, Incenter, Tangent.

Triangle Area, 30 Degrees, Incircle

Geometry Problem 619
Triangle Area, 30 Degrees, Incircle, Incenter, Tangent.

Three Rectangles, Centers, Angles

Geometry Problem 620
Three Rectangles, Diagonals, Centers, Angles.

Two Parallelograms, Center, Parallel

Geometry Problem 621
Three Rectangles, Diagonals, Centers, Angles.

Intersecting Circles

Geometry Problem 622
Square with Perpendiculars, Transversal, Congruence.

Triangle, Incenter, Excenter, Concyclic Points

Geometry Problem 623
Triangle, Incenter, Excenter, Incircle, Excircle, Concyclic Points.

Triangle, Incenter, Excenter, Similarity

Geometry Problem 624
Triangle, Incenter, Excenter, Incircle, Excircle, Similarity.

Triangle, Parallel, Angle Bisector

Geometry Problem 625
Triangle, Parallel Lines, Congruence, Angle Bisector.

Triangle, Incenter, Excenter, Distance

Geometry Problem 626
Triangle, Distance from the Incenter to an Excenter.

Cyclic quadrilateral, Congruence, and Concyclic Points

Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points.

Cyclic quadrilateral, Congruence, Parallel

Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines.

Triangle, Perpendicular, Intersecting Lines

Geometry Problem 629
Triangle, Perpendicular to Sides, Intersecting Lines, Altitude.

Clawson Point

Geometry Problem 630: Clawson Point.
Orthic and Extangents Triangles, Concurrent lines.

Triangle, Angle Bisectors, Collinear

Geometry Problem 631.
Triangle, Exterior Angle Bisectors, Collinear Points.

Triangle, Angle Bisectors, Midpoint, Collinear

Geometry Problem 632.
Triangle, Interior and Exterior Angle Bisectors, Midpoints, Collinear Points.

Triangle, Parallel Lines, Intersecting Lines

Geometry Problem 633
Triangle, Parallel Lines, Intersecting Lines.

Right triangle, Altitude, Incenter, Area

Geometry Problem 634
Right Triangle, Altitude, Incenters, Areas.

Semicircle, Perpendicular, Inscribed Circle, Radius

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

Semicircle, Perpendicular, Inscribed Circle, Tangent

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

Semicircle, Perpendicular, Inscribed Circle, Tangent, Chord

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

Arbelos, Circle, Concyclic Points

Geometry Problem 638
Arbelos and Inscribed Circle: Concyclic Points.

Semicircle, Perpendicular, Inscribed Circle, Tangent, Congruence

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

Archimedes Book of Lemmas Proposition 1

Geometry Problem 640.
Archimedes Book of Lemmas: Proposition 1
Tangent circles and parallel diameters 

Archimedes Book of Lemmas Proposition 2

Geometry Problem 641.
Archimedes Book of Lemmas: Proposition 2
Semicircle, Tangent, Perpendicular, Midpoint.

Archimedes Book of Lemmas Proposition 3

Geometry Problem 642.
Archimedes Book of Lemmas: Proposition 3
Semicircle, Perpendicular, Arc, Midpoint, Congruence.

Archimedes Book of Lemmas Proposition 4

Geometry Problem 643.
Archimedes Book of Lemmas: Proposition 4
Semicircle, Circle, Perpendicular, Arbelos, Area.

Archimedes Book of Lemmas Proposition 5

Geometry Problem 644.
Archimedes Book of Lemmas: Proposition 5
Semicircle, Circle, Perpendicular, Arbelos, Archimedean Twins.

Archimedes Book of Lemmas Proposition 6

Geometry Problem 645.
Archimedes Book of Lemmas: Proposition 6
Semicircle, Circle, Perpendicular, Arbelos, Inscribed Circle.

Archimedes Book of Lemmas Proposition 7

Geometry Problem 646.
Archimedes Book of Lemmas: Proposition 7
Square,Inscribed and Circumscribed Circles, Area.

Archimedes Book of Lemmas Proposition 8

Geometry Problem 647.
Archimedes Book of Lemmas: Proposition 8
Angle trisection. Neusis construction.

Archimedes Book of Lemmas Proposition 9

Geometry Problem 648.
Archimedes Book of Lemmas: Proposition 9
Perpendicular chords, Arcs.

Archimedes Book of Lemmas Proposition 10

Geometry Problem 649.
Archimedes Book of Lemmas: Proposition 10
Tangent, Chord, Parallel, Midpoint.

Tangent Circles

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

Archimedes Book of Lemmas Proposition 11

Geometry Problem 651.
Archimedes Book of Lemmas: Proposition 11
Perpendicular chords, Arcs, Radius.

Archimedes Book of Lemmas Proposition 12

Geometry Problem 652.
Archimedes Book of Lemmas: Proposition 12
Perpendicular chords, Arcs, Radius.

Archimedes Book of Lemmas Proposition 13

Geometry Problem 653.
Archimedes Book of Lemmas: Proposition 13
Circle, Chord, Perpendicular, Congruence.

Archimedes Book of Lemmas Proposition 14

Geometry Problem 654.
Archimedes Book of Lemmas: Proposition 14
Salinon, Semicircles, Diameter, Circle, Area.

Archimedes Book of Lemmas Proposition 15

Geometry Problem 655.
Archimedes Book of Lemmas: Proposition 15
Circle, Inscribed Regular Pentagon, Radius.

Triangle, Cevian, Concurrent Lines

Geometry Problem 656.
Triangle, Cevian, Concurrent Lines.

Triangle, Incircle, Parallel

Geometry Problem 657.
Triangle, Incircle, Tangency Points, Parallel Lines, Congruence.

Triangle, Altitudes, Circles, Angles

Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles.

Parallelogram, Parallel lines, Collinear points

Geometry Problem 659.
Parallelogram, Parallel Lines, Collinear Points.

Triangle, Circle, Diameter, Perpendicular

Geometry Problem 660.
Triangle, Circle, Diameter, Perpendicular Lines.

Intersecting Circles

Geometry Problem 661.
Intersecting Circles, Centers, Secant, Parallelogram.

Triangle Centers, Angles

Geometry Problem 662.
Triangle, Incenter, Circumcenter, Orthocenter, Circle, Angle, Measurement.

Triangle, 60 Degrees, Concurrent lines

Geometry Problem 663.
Scalene Triangle, 60 Degrees, Altitude, Angle Bisector, Perpendicular Bisector, Concurrent lines.

Triangle, 60 Degrees, Centers, Angles

Geometry Problem 664.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Angles, Triangle centers.

Intersecting circles

Geometry Problem 665.
Intersecting Circles, Secant, Tangent, Angles, Mind Map.

Intersecting circles

Geometry Problem 666.
Intersecting Circles, Secant, Tangent, Concyclic points, Mind Map.

Intersecting circles, Tangent, Metric Relations

Geometry Problem 667.
Intersecting Circles, Secant, Tangent, Metric Relations, Mind Map.

Right triangle, Incircles

Geometry Problem 668.
Right triangle, Incircles, Parallel, Common Tangent, Mind Map.

Triangle, Circumcircle, Incenter

Geometry Problem 669.
Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map.

Triangle, 60 Degrees

Geometry Problem 670.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Congruence.

Geometry problem: Triangle, Angles, Congruence

Geometry Problem 671.
Triangle, Cevian, Angles, Congruence.

Tangent Circles, Geometric Mean

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

Tangent Circles, Chord, Metric Relations

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

Triangle, Altitude, Angles

Geometry Problem 674.
Triangle, Altitude, Angles.

Collinear points, Intersecting circles

Geometry Problem 675.
Intersecting Circles, Secant, 45 and 90 Degrees, Collinear Points.

Circles, Diameter, Tangent, Metric Relations

Geometry Problem 676.
Circles, Diameter, Tangent, Chord, Metric Relations.

Parallelogram, Midpoint, Diagonal

Geometry Problem 677.
Parallelogram, Midpoint, Diagonal, Metric Relations.

Simson Line, Parallel

Geometry Problem 678.
Triangle, Simson Line, Circumcircle, Tangent, Parallel, Perpendicular, Collinear Points.

Triangle, Circle, Median, Proportion

Geometry Problem 679.
Triangle, Circle, Median, Proportion.

Concentric Circles

Geometry Problem 680.
Concentric Circles, Radii, Chords, Perpendicular, Metric Relations.

Gergonne Point Theorem

Geometry Problem 681: Gergonne Point.
Triangle, Incircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Gergonne Point Theorem

Geometry Problem 682: Gergonne External Point.
Triangle, Excircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Nagel Point

Geometry Problem 683: Nagel Point.
Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Outer Nagel Point

Geometry Problem 684: Outer Nagel Point.
Triangle, Excircles, Incircle Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Isosceles triangl 100-40-40 degrees

Geometry Problem 685
Isosceles Triangle, 100-40-40 Degrees, Angles, Congruence.

Triangle, Excircles, Tangent

Geometry Problem 686.
Triangle, Three Excircles, Tangency points, Tangent lines, Semi-perimeter, Congruence.

Triangle, Excircles, COncurrency

Geometry Problem 687.
Triangle, Three Excircles, Tangency points, Concurrent Lines
.

Geometry Problem 688, Triangle, 60 Degrees, Mind Map

Geometry Problem 688.
Triangle, Angles, 10, 20, 30, 40, 60 Degrees, Measure, Mind Map, Polya
.

Triangle, Excircles, Tangent, Concurrency

Geometry Problem 689.
Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines, Mind Map.

Distance between the incenter to the centroid

Problem 690: Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.

Isosceles triangle 80, 20, 20 degrees

Geometry Problem 691.
Isosceles Triangle, 80-80-20 Degrees, Angles, Congruence, Mind Map, Polya
.

Quatrefoil, Circle, Square, Area

Geometry Problem 692.
Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya.

Circle, Square, Area

Geometry Problem 693.
Square, Inscribed and Circumscribed Circle, Areas, Mind Map, Polya.

Circle, Square, Area

Geometry Problem 694.
Triangle, Angles, 30 Degrees, Auxiliary Construction, Mind Map, Polya.

Circle, Square, Area

Geometry Problem 695.
Triangle, Quadrilateral, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Circle, Square, Area

Geometry Problem 696.
Triangle, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Square, Circle, Area

Geometry Problem 697.
Square, Circle, Sector, Segment, Tangent, Inscribed, Congruence, Mind Map, Polya.

Quadrilateral, 120 degrees, Angles

Geometry Problem 698.
Quadrilateral, Diagonal, Angle Bisector, Triangle, 120 Degrees.

Equilateral triangle, Circle

Geometry Problem 699.
Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations.

Equilateral triangle, Circle

Geometry Problem 700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of a side, Metric Relations.




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