Proof method: It is known that m is the midpoint of arc AC, MG and vertical chord BC. Proof: CG=AB+BG Proof: Extend AB to E to make GB=BE, and then connect the blue line segments to get CM=AM∠MCB=∠MAE (the circumferential angle of the same arc).
∠ MBE =∠ MCA (∠ MBA+∠ MBE = ∠ MBA+∠ MCA =180 degrees) =∠MAC=∠MBC, so the triangle MGB is all equal to the triangle MEB, so me.
The theorem of string, the third square, is equal to the following equation, the sum of two squares, cosine times two sides, and twice. Chord tangent angle theorem, fillet is equal. The tangent and the inner chord form a chord tangent angle. The theorem of intersecting chords, on the intersecting circle of two chords. The intersection is divided into two sections and the multiplication is equal.
The history of the broken string theorem;
Archimedes is one of the greatest mathematicians in history. He, Newton and Gauss are also called the Three Princes of Mathematics. If we compare their brilliant achievements with the background of the times, or compare their far-reaching influence on the present and future generations, Archimedes should be the first to be promoted. He was even honored as "the God of Mathematics".
The Complete Works of Archimedes compiled by British Heath has no income. Of course, in China, 1998, according to the Chinese version of The Complete Works of Archimedes translated by Zhu Enkuan and Li Wenming by Heath, Ye Yanrun and Chang Xinyi, Archimedes' broken string theorem was not included. Although this complete collection does not include the broken string theorem, it is introduced in some competition books.
The Arabic translation retains the content of Archimedes' theorem of broken strings. 1964, the Soviet Union published the Russian version of The Complete Works of Archimedes based on Al-biruni. The first topic was Archimedes' broken string theorem.