Question

A triangle ABC is inscribed in a circle, and the tangent at C to the circle is parallel to the bisector of angle ABC. Find the magnitude of $\angle CBD$, where D is the point of intersection of the bisector of angle ABC with AC.

Answer 1

According to the alternate segment theorem, angle between a tangent and a chord through a point of contact is equal to the angle in the alternate segment.

$⟹\angle BCX=\angle BAC={40}^{\circ }$

Given $BD\parallel XY$

$⟹\angle DBC=\angle BCX={40}^{\circ }$