Arc of a Circle

Prove angles inscribed in the same arc are congruent.

The inscribed angle in an arc of a circle if its vertex is out side the circle.

In the given circle arc $PQR\cong \text{arc} STU$ and if chord $PR=5 \mathrm{cm}$, then find the value of chord $SU$ in $\mathrm{cm}$.

Prove that the chords corresponding to congruent arcs of a circle are congruent.

In the given circle chord $AC\cong \text{Chord} DF$. If $OC=OD$ and arc $ABC=4 \mathrm{cm}$, find the value of arc $DEF$ in $\mathrm{cm}$.

Prove that corresponding arcs of congruent chords of a circle are congruent.

In the circle, the points $P,Q, R, S$ and $T$ are concyclic, then how many common point(s) do arc $PQR$ and arc $RST$ have if $m\left(\text{arc} PRT\right)=m\left(\text{arc} PQR\right)+m\left(\text{arc} RST\right)$

If the measure of the angle and the length of the radii of two arcs are equal, then the arcs are _____

Two arcs can be called congruent only and only if they have the same degree measure.

What is the central angle of a circle?

If the $m\angle PQR=60° \& m\angle PSR=k°$, then find the value of $k$.

Prove that angles inscribed in the semi circle are right angle.

Prove that angles inscribed in the same circle are congruent.

If the measure of angle $m\stackrel{⏜}{AC}=k°$, then find the value of $k$.

If the measure of angle $m\stackrel{⏜}{AC}=k°$, then find the value of $k$.

If the measure of angle $m\angle B=k°$, then find the value of $k$.

If the measure of angle $m\angle B=k°$, then find the value of $k$.

If the measure of angle $m\angle B=k°$, then find the value of $k$.

In the following figure, $O$ is the centre of the circle. $\angle ABC$ is inscribed in arc $ABC$ and $\angle ABC=65°$. Find the measure of $\angle AOC$.

In the adjoining figure, $\mathrm{O}$ is the centre of the circle. If $\angle \mathrm{ABC}={20}^{\circ }$,then $\angle \mathrm{AOC}$ equal to