Circle Practice Questions with Solutions – Level 1

An arc $AB$ subtends an angle of $110^\circ$ at the center $O$ of a circle. What is the measure of the angle subtended by the same arc at any point $C$ on the major arc of the circle?

In a circle with center $O$, points $A, B, C,$ and $D$ lie on the circumference such that $ABCD$ is a cyclic quadrilateral. If $\angle ABC = 108^\circ$, find $\angle ADC$.

$AB$ is a diameter of a circle with center $O$. $C$ is a point on the circumference such that $\angle BAC = 35^\circ$. What is the measure of $\angle ABC$?

In a cyclic quadrilateral $ABCD$, side $AB$ is extended to a point $E$. If external angle $\angle CBE = 82^\circ$, what is the measure of $\angle ADC$?

In a circle with center $O$, chords $AB$ and $CD$ intersect at an internal point $P$. If $\angle AOC = 50^\circ$ and $\angle BOD = 70^\circ$ (where $A, C, B, D$ lie in cyclic order), find $\angle APC$.

Points $A, B, C, D$ lie on a circle in order. If $\angle ADB = 42^\circ$, what is the measure of $\angle ACB$?

$AB$ is a chord of a circle subtending a central angle of $80^\circ$. $P$ is a point on the minor arc $AB$. What is $\angle APB$?

In a circle, arc $AB$ is one-sixth of the total circumference. What is the measure of the angle subtended by arc $AB$ at any point on the remaining part of the circle?

$A, B, C$ are three points on a circle with center $O$. If $\angle AOB = 90^\circ$ and $\angle BOC = 120^\circ$, find $\angle ABC$ assuming $O$ lies inside $\triangle ABC$.

In a circle, $PQ$ is a chord equal to the radius $R$ of the circle. What is the angle subtended by $PQ$ at the major circumference?