Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### Circle and Angles Transcription
#### Problem 3
**Diagram Explanation:**
A circle is given with points labeled P, Q, and R on its circumference. A line segment PQ is drawn from point P to point Q, and another line segment PR is drawn from point P to point R. The interior point S is marked where the two line segments intersect the circle again at R and Q respectively.
**Mathematical Notation and Question:**
\[ m \angle PQR = \underline{\hspace{5cm}} \]
**Question:**
Calculate or provide the measure of angle PQR based on the given circle and its segments.
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This image and associated question are meant to help students understand the relationships and angle measures within a circle. The terms and points labeled (P, Q, R, S) are utilized in typical geometric problems to illustrate properties of circles, angles, and intersecting line segments.
Remember, the measure \( m \) of an angle is typically found using various geometric theorems and properties related to circles, such as the Inscribed Angle Theorem, which is essential in solving such problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F930d7974-4794-47f1-b792-8faf44a50acb%2F75cb19f7-954c-4661-82f2-b1615f1e64aa%2Fdm45kc_processed.jpeg&w=3840&q=75)
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