Draw 2 diameters MN and DF in a circle. Prove that chords MD and NF are equal.

МН and DF are diameters of a circle, then ОМ = ОН = ОD = OF = R.
In triangles ОМD and ОНF, the angle MOD = HOF as vertical angles, then the triangles ОМD and ОНF are equal on two sides and the angle between them, and then МН = DF, which was required to prove.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.