Triangles: Theorems and Problems 39

Mittenpunkt Point
Triangle center 

Problem 1.
Triangle, median, angles, 45 degrees.

Problem 2.
Triangle, angles, 10, 20 , 30 , 80 degrees.

Problem 3.
Triangle, Angles, 45 degrees, Auxiliary Lines.

Problem 5.
Triangle, cevian, equal segments, angles, cevian.

Problem 6.
Triangle, cevian, equal segments, and angles.

Problem 7.
Triangle, cevian, congruence, and angles.

Problem 8.
Triangles, equal segments, angles, 45 degrees.

Problem 9.
Triangles, equal segments, angles, 30 degrees.

Problem 10.
Triangle, cevian, equal segments, angles, 80-20 degrees.

Equilic Quadrilateral.
Equilateral triangles. 

Nagel Point Theorem. Proof.
Triangle center. 

Puzzle of the Nagel Point: 22 pieces of polygons.

Semiperimeter and excircles of a triangle.

Semiperimeter and incircle of a triangle.

Semiperimeter, incircle and excircles of a triangle.

Gergonne Point Theorem. Concurrency. Interactive proof with animation.

Key concept: Ceva's Theorem.
 

Ceva's Theorem. Triangle, Concurrency. Interactive proof with animation. Key concept: Menelaus Theorem.

Puzzle of the Ceva's Theorem: 48 classic piece.

Menelaus' Theorem. Interactive proof with animation and key concepts.