Problem 501.
Triangle, Two Squares, Center, Midpoint, another Square.
Problem 502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure.
Problem 503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency.
Problem 504.
Equilateral Triangle, Angles, 45, 60 Degrees.
Problem 505.
Right Triangle, Cevian, Sum of Segments, Angles.
Problem 506.
Triangle with Three Squares, Center, Midpoint, Perpendicular.
Problem 507.
Triangle, Interior Point, 120 Degrees, Congruence, Angle.
Problem
508.
Triangle with three Squares, Four triangle of equal Area.
Problem 509.
Triangle, 120 Degrees, Angles, Congruence, Mind Map.
Problem 510.
Triangle, Three Squares, Midpoints, Concurrency.
Problem 511.
Triangle, Double Angle, Angle Bisector, Measure.
Problem 512.
Triangle with three squares and concurrency.
Problem 513.
Triangle, Double Angle, Exterior Angle Bisector, Measure.
Problem 514.
Triangle, Five Squares, Line, Area.
Problem 515.
Triangle, Double Angle, Altitude, Measure.
Problem 516.
Triangle, Cevian, Congruence, Angles.
Problem
517.
Right Triangle, Six Squares, Areas.
Problem 518.
Parallelogram, Five Squares, Centers, 45 Degrees, Measure.
Problem 519.
Triangle, Squares, Altitude, Perpendicular, Rectangle, Area.
Problem 520.
Triangle with six Squares, Ratio, Area.
Problem 521.
Triangle with three Squares, Altitude, Rectangle, Area.
Problem 522.
Right Triangle, Circle, Diameter, Tangent.
Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity.
Problem 524.
Circle, Equilateral Triangles, Midpoint, Side, Measurement.
Problem 525.
Circles, Diameter, Tangent, Radius, Congruence, Measurement.
Problem 526.
Equilateral Triangle, Chord, Measurement.
Problem
527.
Circle, Tangent, Secant, Chord, Midpoint, Measurement.
Problem 528.
Triangle, Medians, Perpendicular, Measurement.
Problem 529.
Right Trapezoid, Circle, Diameter.
Problem 530.
Right Trapezoid, Circle, Diameter.
Problem 531.
Triangle, Angle Bisector, Midpoint, Parallel, Perimeter, Semiperimeter.
Problem 532.
Triangle, Circumcircle, Equal Angles, Perpendicular, Area.
Problem
533.
Euclid's
Elements, Book XIII, Proposition 10.
Problem
534.
Right Triangle, Squares, Perpendicular, Dissection, Areas.
Problem
535.
Sawayama - Thebault's theorem: Triangle, Incircle, Circle, Center, Tangent,
Collinear.
Problem
536.
Intersecting Circles, Chord, Perpendicular.
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Problem
537.
Rectangle, Midpoints, Diagonal, Angle Bisector.
Problem
538.
Triangle, Perpendicular Bisector, Circumcircle, Midpoint.
Problem
539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.
Problem
540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.
Problem
541.
Right Triangle, Altitude, Angle Bisector, Congruence.
Problem
542.
Right Triangle, Altitude, Angle Bisector, Perpendicular, 90 Degrees.
Problem
543.
Right Triangle, Altitude, Angle Bisector, Median.
Problem
544.
Right Triangle, Altitude, Median, Equal angles, Measure.
Problem
545.
Acute Triangle, Squares, Altitudes, Area, Measure.
Problem
546.
Triangle, Angle Trisectors, 60 Degrees, Equilateral triangle.
Problem
547.
Triangle, Transversal, Four Circumcircles, Concurrency.
Problem
548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points,
Similarity.
Problem
549.
Parallel lines, Transversal, Angle Sums.
Problem
550.
Parallel lines, Transversal, Angle Sums.
Problem
551.
Parallel lines, Transversal, Angle Sums.
Problem
552.
Parallel lines, Transversal, Angle Sums.
Problem
553.
Quadrilateral, Angles, Sum.
Problem
554.
Concave Quadrilateral, Angles, Sum.
Problem
555.
Parallel lines, Angle Sums.
Problem
556.
Quadrilateral, Diagonal, Angles, Auxiliary Lines.
Problem
557.
Quadrilateral, Midpoints, Sides, Varignon Parallelogram, Area, Auxiliary Lines.
Problem
558.
Quadrilateral, Trisection, Sides, Wittenbauer Parallelogram, Area, Auxiliary Lines.
Problem
559.
Triangle, Cevian, Incenters, Angle, 90 Degrees.
Problem
560.
Triangle, Cevian, Incenter, Incircle, Perpendicular, Tangent.
Problem
561.
Triangle, Cevian, Incenter, Incircle, Perpendicular, Tangent.
Problem
562.
Triangle, Cevian, Incenter, Perpendicular, Concyclic Points, Cyclic
Quadrilateral.
Problem
563.
Regular Pentagon, Center, Rectangle, Diagonals, Angle.
Problem
564.
Complete Quadrilateral, Incenter, Excenter, Concyclic Points.
Problem
565.
Triangle, Isogonal lines, Angles, Congruence, Concyclic Points.
Problem
566.
Quadrilateral, Diagonals, Parallel.
Problem
567.
Right triangle, Incircle, Excircle, Collinear tangency points.
Problem
568.
Triangle, Excircles, Tangency Point, Congruence.
Problem
569.
Quadrilateral, Excircles, Tangency Points, Congruence.
Problem
570.
Square, Center, Right Triangles, Congruence, Collinearity.
Problem
571.
Circle, Diameter, Chord, Perpendicular, Measurement.
Problem
572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles.
Problem
573.
Cyclic quadrilateral, Angle bisector, Perpendicular.
Problem
574.
Circle, Chord, Secant, Angle Bisector, Perpendicular.
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Problem
575.
Cyclic quadrilateral, Angle bisector, Measurement.
Problem
576.
Centroid, Triangle, Quadrilateral, Parallel, Measurement.
Problem
577.
Isosceles triangle, Midpoint, Perpendicular, Concyclic points, Circle.
Problem
578.
Circle, Perpendicular Chords, Midpoints, Curvilinear Triangle, Area, 90 Degrees.
Problem
579.
Quadrilateral, Diagonals, Triangles, Areas.
Problem
580.
Triangles, Equal Angle, Transversal, Product of Sides, Areas.
Problem
581.
Volume of two Triangular Pyramids, Equal Trihedral Angle, Product of three Edges.
Problem
582.
Quadrilateral, Diagonals, Incenters, Metric Relations.
Problem
583.
Quadrilateral, Diagonals, Circumcenters, Parallelogram, Octagon, Areas.
Problem
584.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms.
Problem
585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency.
Problem
586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.
Problem
587.
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Distance, Half the Difference.
Problem
588.
Triangle, Incenter, Incircle, Tangency Points, Midpoints, Distance, Sum.
Problem
589.
Triangle, Incenter, Incircle, Tangency Points, Midpoint, Perpendicular, Distance.
Problem
590.
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Areas.
Problem
591.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude.
Problem
592.
Triangle, Incenter, Incircle, Tangency Point, Midpoints, Concurrent Lines, Congruence.
Problem
593.
Triangle, Circumcircle, Collinear Points.
Problem
594.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude, Angle, Half the Difference.
Problem
595.
Triangle, Equal Angles, Isogonal Conjugate, Similarity.
Problem 596
Quadrilateral, Right Triangle, Isosceles, Midpoint.
Problem 597
Quadrilateral, Right Triangle, Isosceles, Angle, Congruence.
Problem 598.
Trapezoid, Perpendicular, Equal Angles, Metric Relation.
Problem 599
Regular Hexagon, Square, Midpoint, Angle, Degrees.
Problem
600
Circle, Area, Tangent, Semicircle, Tangency Point.
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