Math Olympiad Amazing Geometry Puzzle of Area, solved by Dozens of Math tools!

This video demonstrates how to tackle a hard area problem by nearly every single technique in Math problem solving: from coordinate geometry to deductive geometry, from vectors to Cosine Formula, from shoelace formula to Ptolemy's Theorem. It is a journey of integrating various disciplines in an interesting question, which we can see the scenario from a wide range of perspectives!

Chapters:
00:00 The Problem Setting
00:32 Overview of Strategies
01:01 Coordinates of Points
02:28 Equations of Semi-Circles
04:54 Two methods to find area
07:09 Shoelace Formula
08:32 Why the Centre of Square?
09:39 Congruent Triangles
10:58 Intersection point of Semi-Circles
11:48 Equations of Straight Lines
12:50 Vectors
13:10 Section Formula
14:28 Similar Triangles
15:53 Cyclic Quadrilateral
17:10 Cosine Formula
17:39 Quadratic Formula
18:47 Ptolemy's Theorem
19:26 Final method for area

Check out other interesting Math videos in the following playlists:
Algebra:    • Algebra  
Geometry:    • Geometry  
Trigonometry:    • Trigonometry  
Calculus:    • Calculus  
Number Theory:    • Number Theory  
30-day CHALLENGE of Integration by Parts:    • 30-day CHALLENGE of Integration by Parts