Question

Which among the following statements is/are correct for the figure given below?

• A. $AD=BC$
• B. $\angle ADB=\angle BCA$
• C. $\angle AOD=\angle DOC$
• D. $OD=OA$

Answer 1

Answer: (A), (B)

The correct options are
A $AD=BC$
B $\angle ADB=\angle BCA$

For triangles, $△ADO\text{and}△BCO$,
$OA=OB$ ..... (given)
$DO=CO$ ..... (given)
$\angle AOD=\angle BOC$ ..... (vertically opposite angles)
$\therefore △ADO\cong △BCO$ .... (SAS criterion for congruency)

Hence,
$AD=BC$ (corresponding parts)
$\angle ADO=\angle BCO$
$\text{or}\angle ADB=\angle BCA$ ....(corresponding parts)