Question

Is there any condition in the above figure that $△ABC$ is congruent to $△DBC$ given that $BC$ must not be diameter?

• A. YES
• B. NO

Answer 1

The correct option is B NO

As $BC$ is not the diameter so it is a chord which is dividing the circle into two segments one is major and another is minor so there CANNOT be any condition for which the triangles are congruent in the above figure because angle made by the same chord in the major segment is always less than the angle made by the chord in the minor segment.
So, $\angle BAC<\angle BDC\left(\angle Aisonmajorsegmentand\angle Donminorsegment\right)$

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