What is an angle whose vertex is on a circle and whose sides contain chords of a circle

1. What is an angle whose vertex is on a circle and whose sides contain chords of a circle?
   A. Central angle
   C. Circumscribe angle
   B. Inscribe angel
   D. Intercepted angle
2. It is a segment joining any two points on the circle.
   A. Chord
   C. Diameter
   B. Radius
   D. Arc
3. Which of the following is the sum of the measures of the central angles of a circle with no common interior points?
   A. 360
   C. 240
   B. 120
   D. 480
4. If an inscribe angle of a circle intercepts a semicircle, then the angle is
   A. Acute
   C. obtuse
   B. right
   D. straight
5. It is an arc of a circle that measures less than a semicircle.
   A. chord
   C. major arc
   B. minor arc
   D. diameter

The Correct Answer and Explanation is :

Here are the answers with explanations:

1. B. Inscribed angle
   An inscribed angle is an angle whose vertex is on a circle, and whose sides contain chords of the circle. This angle is formed by two chords that share a common endpoint, with the vertex located on the circle itself.
2. A. Chord
   A chord is a segment that joins any two points on the circle. It does not necessarily pass through the center of the circle, unlike the diameter. The diameter is a specific chord that passes through the center of the circle.
3. A. 360
   The sum of the measures of the central angles of a circle, with no common interior points, is 360°. This is because the central angles of a circle represent a complete rotation around the center of the circle, and a full rotation is always 360 degrees.
4. B. Right
   If an inscribed angle intercepts a semicircle (meaning the angle subtended by a diameter), the angle will be a right angle (90°). This is a well-known property of circles, sometimes referred to as Thales’ Theorem.
5. B. Minor arc
   A minor arc is an arc of a circle that measures less than a semicircle (less than 180°). The major arc, in contrast, is the larger arc, and it measures more than 180°. The minor arc is the shorter of the two.

Let me create an image for these geometric concepts.

Here is the geometric diagram illustrating the key concepts you mentioned. It visually represents the inscribed angle, chord, central angle, semicircle with the right angle, and the minor arc. Let me know if you need any further clarifications!