Angle splitting theorem is a basic theorem in plane geometry. Zhang Guanglu of Hechi City, Guangxi claimed to be the discoverer and nominator of this theorem. In fact, someone has already discovered this relationship, but it is too simple to call it a theorem.

Many geometric problems involving angle transformation and proportional line segments can be dealt with by splitting angle theorem.

The angular splitting theorem points out that: in △ABC, D is a point on the side of BC that is different from B, C or its extension line; If AD is connected, BD/CD=(sin∠BAD/sin∠CAD)*(AB/AC).

Extended data:

In the plane rectangular coordinate system (Cartesian coordinate system), the horizontal axis and the vertical axis are divided into four regions, and each region is called a quadrant. Mainly used in trigonometry and coordinate system in complex numbers. The quadrant takes the origin as the center and the X axis and Y axis as the dividing line.

The upper right is called the first quadrant, the upper left is called the second quadrant, the lower left is called the third quadrant, and the lower right is called the fourth quadrant. The points on the coordinate axis do not belong to any quadrant.

∫AB/AC = sin∠ACB/sin∠ABC comes from sine theorem.

Sometimes the above formula is written as: BD/CD = (sin ∠ bad/sin ∠ CAD) * (sin ∠ ACB/sin ∠ ABC), so that the ratio of line segments can be completely converted into the ratio of angles.

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