structural:expansion, quality:corruption, linguistic:paraphrasing
Circles

A circle with equation (x − x ∘) 2 + (y − y ∘) 2 = r 2 {\displaystyle \left(x-x_{\circ }\right)^{2}+\left(y-y_{\circ }\right)^{2}=r^{2}} is uniquely determined by three points (x 1, y 1), (x 2, y 2), (x 3, y 3) {\displaystyle \left(x_{1},y_{1}\right),\;\left(x_{2},\,y_{2}\right),\;\left(x_{3},\,y_{3}\right)} not on a line. A simple way to determine the parameters x ∘, y ∘, r {\displaystyle x_{\circ },y_{\circ },r} uses the inscribed angle theorem for circles:

Usually one measures inscribed angles by a degree or radian θ, but here the following measurement is more convenient: