Machu Picchu, Geometry Theorems and Problems, Online Education

Recent Additions 13, Theorems and Problems, Plane Geometry

41. Proposed Problems about congruence of line segments, angles, and triangles.
     Level: High School, SAT Prep, College geometry.
    


42. Ptolemy's Theorem.
    


43. Ptolemy's Extension Cyclic Quadrilateral: Ratio of the Diagonals.
    

 44. Sangaku Problem (An Old Japanese Theorem)

 

Let a convex inscribed polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the triangulation chosen.


 

 

 45. Sangaku Problem 2. Proof



 

 

 46. Sangaku Problem 3

 

3 circles of radiii: a, b, c mutually tangent to each other and a line

 

 

47. Sawayama -Thebault's theorem
    


48. Semiperimeter and excircles of a triangle
    


49. Semiperimeter and incircle of a triangle
    


50. Semiperimeter and incircle and excircles of a triangle
    


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Last updated: November 17, 2007