Triangles: Theorems and Problems 36

Proposed Problem 51: Fagnano's Problem
Inscribed Triangle with the Minimum Perimeter.

Lunes of Hippocrates 4
Right triangle. 

Lunes of Hippocrates 3
Right triangle. 

Lunes of Hippocrates 2
Right triangle. 

Lunes of Hippocrates 1
Right triangle. 

Pythagoras and Circle Area
Right triangle. 

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean, hypotenuse, cathetus (legs), semiperimeter, altitude, median, similar shapes areas, centers, orthocenter, incenter, centroid, circumcenter, radius, inradius, circumradius, exradius, circles, incircle, circumcircle, excircle.

Triangle and Squares 21
See also: Triangle and Squares 19

Triangle and Squares 20

Proposed Problem 50. Triangle with Equilateral triangles.
Seventeen conclusions.

Proposed Problem 49. Angles and right triangle.

Proposed Problem 48. Angles and triangles.

Proposed Problem 47. Angles and triangles.

Proposed Problem 46. Angles and triangles.

Proposed Problem 45. Angles and triangles.

Proposed Problem 44. Angles and triangles.

Proposed Problem 43. Angles and triangles.

Proposed Problem 42. Angles and triangles.

Proposed Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances.

Adams' Circle Theorem
 

Spieker Center
Triangle center.

Proposed Problem 39.
Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles.