Two diameters AD and BC are drawn in the circle. prove that the chords AC and BD are equal.
| July 23, 2021 | education
Consider triangles AOC and BOD.
Triangles AOC and BOD are isosceles, since OA = OC = OB = AD, as the radii of a circle.
The angle AOC of the triangle AOC is equal to the angle DOB of the triangle DOB as the vertical angles at the intersection of the diagonals AD and CB. Then the triangles AOC and BOD are equal in two sides and the angle between them, the second criterion for the similarity of triangles, and therefore AC = BD, which was required to be proved.
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