In a circle with center O, two equal chords AB and CD are drawn. Prove that the angles OAB and ODC are equal.

univerkov | March 13, 2021 | education

Let’s build the radii OA, OB, OС and OD.

By condition, the chords AB and CD are equal, AB = CD.

Then in triangles AOB and COD, AB = CD, OA = OB = OC = OD = R, then triangles AOB and COD are equal on three sides, and therefore the angle AOB = COD as similar angles of equal triangles, which was required to be proved.

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