Question

In which of the following $△ABC\cong △DCB$?

• A.
• B.
  $O$ is centre of the circle.
• C.
• D. None of the above

Answer 1

The correct option is B

$O$ is centre of the circle.
In option $\left(a\right)$,
$BC$ is common in both side
$\angle A=\angle D\text{(Angle made on the same segment by chord BC)}$
but two things are not sufficient to prove tringles congruent.

In option $\left(b\right)$
taking $△ABC$ and $△DCB$
$\angle BAC=\angle CDB\text{(Angle made on the same segment by chord BC)}$
$\angle ABC=\angle DCB={90}^o\text{(Angle made by diameters AC and BD)}$
$BC=BC$ (common in both triangles)
So, $△ABC\cong △DCB$ (AAS)

In option $\left(c\right)$
only side $BC$ is common nothing else is given so triangles in option $\left(c\right)$ are not congruent.

Hence, option $\left(b\right)$ correct.