What is the projective theorem in the mathematical triangle?

Projection theorem of right triangle: It is known that if a, b and c are used to represent the vertices of a right triangle, where A is the right vertex, and the intersection of the vertical line BC with point A as the hypotenuse and the vertical foot is D, then there is AD 2 = BD * CD.

General triangle projective theorem: c = bcosA+acosB；;

b = ccosA+acosC； a=ccosB+bcosC

Prove:

a^2=b^2+c^2-2bccosa； b^2=a^2+c^2-2accosB

Add:

0=2c^2-2bccosA-2accosB，

c=bcosA+acosB