Challenges on Equal Chords and their Distance from Centre

Q.

If arcs$AXB$ and$CYD$ of a circle are congruent, find the ratio of $AB$ and $CD$.

Q. Find the ratio of the distance from the center of the circle to congruent sides of the triangles, if $△AEC\cong △DFB.$

1. $1:1$
2. $2:1$

Q. Determine the angle between the lines passing through the center and bisecting the chords AC and CB.
degrees

Q. The two chord CA and CB are equidistant from the center O. Find the angle ∠B.
degrees

Q. If OM=ON, then what are the length of $\text{AM}$ and value of $\angle \text{OMB}?$

1. $\text{AM}=9$ cm
   $y={90}^{\circ }$
2. $\text{AM}=18$ cm
   $y={60}^{\circ }$
3. $\text{AM}=9$ cm
   $y={60}^{\circ }$
4. $\text{AM}=18$ cm
   $y={90}^{\circ }$