Exercise

If arcs $AXB$ and $CYD$ of a circle are congruent, find the ratio of $AB$ and $CD$.  If the answer is $k:k$, write the value of $k$.

Two chords $AB$ and $AC$ of a circle subtends angles equal to $90°$ and $150°$, respectively at the centre. If $\text{AB}$ and $AC$ lie on the opposite sides of the centre and $\angle \mathrm{BAC}=k°$, then find the value of $k$.

A chord of a circle is equal to its radius. If the angle subtended by this chord at a point in the major segment is $k°$, then find the value of $k.$

In Figure, $\angle ADC=130°$ and chord $BC=$chord $BE$. If $\angle CBE=k°$. Then find the value of k.

In Figure, $\angle \text{ACB}=40°$ and $\angle \text{OAB=k°}$. Then find the value of k.

A quadrilateral $ABCD$is inscribed in a circle such that$AB$ is diameter and $\angle ADC={130}^{°}.$ If $\angle BAC=k°$, then write the value of $k$.

In Figure, $AOB$ is a diameter of the circle and $C,D, E$ are any three points on the semi-circle. If the value of $\angle ACD+\angle BED=k°$. Then find the value of $k$.

In the below figure, $\angle OAB=30°$ and $\angle OCB=57°$. If $\angle BOC-\angle AOC=k°$, then find the value of $k$.