41. Proposed
Problems about congruence of line segments, angles, and triangles.
Level: High School, SAT Prep, College geometry.
![](../problem/problem_170x100.jpg)
42.
Ptolemy's Theorem.
![](../equilic/cyclic_ptolemy_theorem_170.jpg)
43.
Ptolemy's
Extension Cyclic Quadrilateral: Ratio of the Diagonals.
![](../equilic/cyclic_ptolemy_ratio_170.jpg)
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.
![](../sangaku_old_japanese.gif)
|
|
45. Sangaku Problem 2.
Proof
|
3 circles of radiii:
a,
b,
c
mutually
tangent to each other and a line
![](../Sangaku3.gif)
|
|
47.
Sawayama -Thebault's
theorem
![](../problem/sawa_thebault_theorem_170.jpg)
48.
Semiperimeter and excircles of a triangle
![](../semiperimeter_excircle170.jpg)
49.
Semiperimeter and incircle of a triangle
![](../semiperimeter_incircle170.jpg)
50.
Semiperimeter and incircle and excircles of a triangle
![](../semiperimeter_in_exc170.jpg)
|