The segments AB and CD are the diameters of the circle. Prove that: chords BD and AC are equal.
| August 13, 2021 | education
Let point O be the center of the circle (and the point of intersection of the diameters AB and CD).
Consider triangles ACO and BDO:
CO = DO (these are the radii of the circle),
BO = AO (these are also the radii of the circle),
the SOA angle is equal to the DOB angle (vertical angles).
Therefore, triangles ACO and BDO are equal (on two sides and the angle between them).
Hence, BD = AC.
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