Question

In a circle with centre O, diameter AD and diameter BC are given. Prove that chord AB $\cong$ chord CD.

Answer 1

Draw a circle of radius $r$ and draw diameters $AD$ and $BC$ and then join $AB$ and $CD$ as shown in the figure.

In $△AOB$ and $△COD$ ,

$AO=DO$ (radius)

$BO=CO$ (radius of circle)

$\angle AOB=\angle DOC$ (opposite angles)

Hence, $△AOB\cong △DOC$ (by SAS)

$\Rightarrow AB\cong CD$ {By c.p.c.t.}