Circles

Two concentric circles have the:

The radii of two congruent circles must be:

A chord that is not a diameter divides a circle into two segments of _____ sizes.

A chord $LM$ subtends an angle of $21^\circ$ at the circumference in the major segment. What is the angle subtended by the same chord at the center?

In a circle, arc $ABC$ subtends an angle of $108^\circ$ at the center. Find the measure of the angle subtended by the same arc at the circumference in the major segment.

What is the name of the longest chord of a circle that subtends a $90^\circ$ angle at any point on the circumference?

A perpendicular from the centre to a chord of length $16$ cm is $6$ cm long. What is the diameter of the circle?

If $OM \perp AB$ in a circle with centre $O$, and the radius is $17$ cm and $OM = 8$ cm, find the length of chord $AB$.

In a circle of radius $29$ cm, find the length of a chord which is at a distance of $21$ cm from the centre.

In the construction of a circle passing through three non-collinear points, why do we use perpendicular bisectors?

The center of the circle passing through $A(0,0), B(4,0),$ and $C(0,4)$ is:

If point $O$ is the center of the unique circle passing through $A, B,$ and $C$, then which line segments are equal?

Two chords $A$ and $B$ are at the same distance from the centre. If the length of chord $A$ is $9$ cm, what is the sum of the lengths of chord $A$ and chord $B$?

Chords $LM$ and $NP$ are both $19$ cm long. If the distance from the centre to $LM$ is $4.4$ cm, then the distance to $NP$ is:

If $3$ times the distance of chord $A$ from the centre equals $3$ times the distance of chord $B$ from the centre, then:

In a cyclic quadrilateral $ABCD$, if $\angle A = 50^\circ$ and $\angle B = 80^\circ$, find $\angle D$.

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

If $\angle XOY = 120^\circ$ at the center, find the angle at the circumference in the minor segment.

In a cyclic quadrilateral $PQRS$, if $\angle P = 80^\circ$ and $\angle Q = 80^\circ$, find the measure of $\angle R$.

If $\angle B = 130^\circ$ in a cyclic quadrilateral $ABCD$, find the exterior angle formed by producing side $AB$ at vertex $B$.

In cyclic quadrilateral $ABCD$, if $\angle A$ is $\frac{1}{5}$ of $300^\circ$, find the measure of $\angle C$.