Point О the center of the circle, the angle COD = the angle of the MOK, prove that the chords CD and MK are equal.

univerkov | July 1, 2021 | education

Let’s build the radii OK, OM, OС and OD.

Then the triangles MOK and COD are isosceles with the bases MK and CD.

In triangles MOK and COD, the sides OM = OK = OC = OD = R.

By condition, the angle COD = MOK, then the triangles MOK and COD are equal on two sides and the angle between them, according to the first sign of equality of the triangles.

Then the chord MK is equal to the chord CD, as required.

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