Question

What conclusion can be drawn from the figures of each part if
a. DB is the bisector of $\angle ADC?$

b. BD bisects $\angle ABC?$

c. DC is the bisector of $\angle ADB,CA\perp DAandCB\perp DB?$

Answer 1

a. Since, DB is the bisector of $\angle ADC,$ then $\angle ADB=\angle CDB$

b. We know that in a parallelogram, diagonals bisect the opposite angles.

So, $\angle CBD=\angle ABD$
Hence, BD bisects $\angle ABC$
c. In a circle, radii of a circle drawn from the point of tangent are perpendicular and line segment joining the centre of the circle to the outer point D bisects the angle formed by the tangents at outer point D.

The, DC is a bisector of $\angle ADB$ and CA $\perp$ AD and CB $\perp$ BD