Question

In the given figure, $OA=OB,OC=OD,\angle AOB=\angle COD.$ Which of the following statements is true$?$

• A. $AC=CD$
• B. $OA=OD$
• C. $AC=BD$
• D. $\angle OCA=\angle ODC$

Answer 1

The correct option is C $AC=BD$

In $△$s $AOC$ and $BOD$
$OA=OB$ (Given)
$OC=OD$ (Given)
$\angle AOB-\angle COB=\angle COD-\angle COB,$
i.e., $\angle AOC=\angle BOD$
$\therefore$ $△AOC\cong △BOD$ (SAS)
$\Rightarrow$ $AC=BD$ (cpct)