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Which of the following is NOT a property of a chord?

What term describes the perimeter of a circle?

If a radius of a circle is 5 cm, what is the diameter of the circle?

A line is drawn from the center of a circle to the midpoint of a chord. Which statement accurately describes the relationship between the line and the chord?

What is the relationship between the angle at the center of a circle and the angle at the circumference subtended by the same arc?

In a cyclic quadrilateral, what is the sum of a pair of opposite angles?

If two tangents are drawn to a circle from the same external point, what can be said about the lengths of the tangents from the external point to the points of tangency?

In circle geometry, if an arc subtends an angle of $x$ degrees at the center, and the same arc subtends an angle of $y$ degrees at the circumference, express $x$ in terms of $y$.

Consider a cyclic quadrilateral $ABCD$ inscribed in a circle. If angle $ABC$ is $100$ degrees, what is the measure of angle $ADC$?

Imagine two circles intersecting at points $P$ and $Q$. A line through $P$ intersects the circles at $A$ and $B$, respectively, and a line through $Q$ intersects the circles at $C$ and $D$, respectively. If $AC$ and $BD$ do not intersect inside either circle, and points $A$, $C$, $B$, and $D$ are concyclic, ascertain the relation between $AC$ and $BD$.

Which of the following terms accurately describes a straight line segment that connects two points on the circumference of a circle?

According to circle geometry theorems, what is the relationship between a tangent line at any point on a circle and the radius drawn to that same point?

If a line drawn from the center of a circle is perpendicular to a chord, what conclusion can be drawn about the chord?

An arc subtends an angle of $60$ degrees at the circumference of a circle. What is the measure of the angle subtended by the same arc at the center of the circle?

Points $A$, $B$, $C$, and $D$ lie on the circumference of a circle. If $\angle ABC = 95^\circ$, what is the measure of $\angle ADC$?

Consider a cyclic quadrilateral $PQRS$. If the exterior angle at vertex $R$ is $70^\circ$, what is the measure of the interior opposite angle at vertex $P$?

From a point $T$ outside a circle, two tangents $TA$ and $TB$ are drawn to the circle, touching it at points $A$ and $B$ respectively. Which of the following statements is always true?

In a circle with center $O$, chord $AB$ subtends $\angle ACB$ at the circumference and $\angle AOB$ at the center. If $\angle ACB = 50^\circ$, and a tangent is drawn at point $A$, forming an angle $\angle CAT$ with chord $AB$. What is the measure of $\angle CAT$?

Consider two equal chords, $PQ$ and $RS$, in a circle with center $O$. If $\angle POQ = 80^\circ$, what is the measure of $\angle ROS$?

Four points $A, B, C, D$ are positioned such that line segment $AB$ subtends equal angles at points $C$ and $D$ on the same side of $AB$. What can be definitively concluded about the points $A, B, C, D$?

What distinguishes a diameter from other chords in a circle?

What is the primary conclusion of the Tangent-Chord Theorem?

If a line segment from the center of a circle bisects a chord that is not a diameter, what can be stated about the line segment and the chord?

In a cyclic quadrilateral $ABCD$, if $\angle ABC = 75^\circ$, what is the measure of $\angle ADC$?

Two chords, $PQ$ and $RS$, in a circle are equidistant from the center. What can be concluded about their lengths?

A circle has a radius of 8 cm. From a point 17 cm away from the center, a tangent is drawn to the circle. What is the length of the tangent?

In a circle, two parallel chords are drawn on opposite sides of the center. If the chords measure 12 cm and 16 cm and the radius of the circle is 10 cm, what is the distance between the two chords?

Consider two circles intersecting at points $A$ and $B$. A line through $A$ intersects the circles at $C$ and $D$, respectively. A line through $B$ intersects the circles at $E$ and $F$, respectively. If $CD$ is parallel to $EF$, what relationship exists between $CE$ and $DF$?

Two circles intersect at points $P$ and $Q$. Tangents to the circles at point $P$ intersect the circles again at points $A$ and $B$, respectively. What is the relationship between the angle $APB$ and the angle formed by the line segment $PQ$?

Within a circle of radius $'r'$, two chords of lengths $'a'$ and $'b'$ intersect at right angles. The distance from the center of the circle to the point of intersection of the chords is $'d'$. Identify the correct relationship between $a$, $b$, $r$, and $d$.

Which term describes a line that intersects a circle at only one point?

What is the defining characteristic of a diameter within a circle?

If a radius of a circle is known, how can the diameter be determined?

What term describes a straight line connecting two points on the circumference of a circle?

If an angle at the center of a circle measures $80$ degrees, what is the measure of the angle at the circumference subtended by the same arc?

In a cyclic quadrilateral $ABCD$, if $\angle A = 60^\circ$ and $\angle B = 120^\circ$, what are the measures of $\angle C$ and $\angle D$, respectively?

Given a circle with center $O$, and a tangent $PA$ touching the circle at $A$. If $\angle OAP = x$, what is the value of $x$?

Two chords $AB$ and $CD$ in a circle are equal in length. If they intersect at point $E$ inside the circle, which of the following statements must be true?

In a circle, chords AB and CD intersect at point E. If $AE = 6$, $EB = 4$, and $CE = 3$, what is the length of ED?

If two circles intersect such that the common chord is the diameter of one of the circles, what can be inferred about the relationship between the centers of the two circles and the point(s) of intersection?