Congruence of Triangles

Q.

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centers.

Q. Two arcs in the circle make the equal angle at the center of the circle. then the two triangles made by the corresponding chord and the radii joint to the end points of arc are

1. Congruent
2. Similar

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

1. YES
2. NO

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

1. 
2. 
   $O$ is centre of the circle.
3. 
4. None of the above

Q.

$△ABC$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. $\angle BCD$ is equal to ____.

Q. Two equal chords of the circle maketriangles when their end points are joined to the center of circle with radii.

Q.
In the given figure, $AB$ and $CD$ are the diameters of circle and $O$ is the centre of the circle. Then, which of the following is correct ?

1. $△AOD\cong △COB$
2. $△ACB\cong △CAD$
3. $\angle ADC=\angle CBA$
4. All of the above

Q. In an isosceles triangle ABC, AB = AC and BA is produced to D, such that AB = AD. What is the value of $\angle BCD$?

Q. In the following figure, $\Delta ABD\cong \Delta ACD$. If $\angle BDC={110}^{\circ }$ and $\angle DAC={30}^{\circ }$, then the measure of angle $\angle DBA$ is.

1. ${70}^{\circ }$
2. ${40}^{\circ }$
3. ${30}^{\circ }$
4. ${25}^{\circ }$