Triangles: Theorems and Problems 14

Carnot's Theorem in an Acute Triangle.

Carnot's Theorem in an Obtuse Triangle.

Geometry Problem 596
Quadrilateral, Right Triangle, Isosceles, Midpoint.

Geometry Problem 595
Triangle, Equal Angles, Isogonal Conjugate, Similarity.

Geometry Problem 594
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude, Angle, Half the Difference.

Geometry Problem 593
Triangle, Circumcircle, Collinear Points.

Geometry Problem 592
Triangle, Incenter, Incircle, Tangency Point, Midpoints, Concurrent Lines, Congruence.

Geometry Problem 591
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude.

Geometry Problem 590.
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Areas.

Geometry Problem 589
Triangle, Incenter, Incircle, Tangency Points, Midpoint, Perpendicular, Distance.

Geometry Problem 588
Triangle, Incenter, Incircle, Tangency Points, Midpoints, Distance, Sum.

Geometry Problem 587
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Distance, Half the Difference.

Geometry Problem 586
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

Problem 583
Quadrilateral, Diagonals, Circumcenters, Parallelogram, Octagon, Areas.

Problem 580
Triangles, Equal Angle, Transversal, Product of Sides, Areas.

Problem 577.
Isosceles triangle, Midpoint, Perpendicular, Concyclic points, Circle.

Problem 576.
Centroid, Triangle, Quadrilateral, Parallel, Measurement.

Problem 572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles.

Problem 568.
Triangle, Excircles, Tangency Point, Congruence.

Problem 567.
Right triangle, Incircle, Excircle, Collinear tangency points.

Problem 565.
Triangle, Isogonal lines, Angles, Congruence, Concyclic Points.