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How do you find the central angle of a circle given the radius and arc length?

Find the Central Angle from the Arc Length and Radius You can also use the radius of the circle and the arc length to find the central angle. Call the measure of the central angle θ. Then: θ = s ÷ r, where s is the arc length and r is the radius.

How do you find the measure of a central angle that intercepts an arc?

Intercepted arc formula

  1. The central angle = the measure of the intercepted arc.
  2. 2 x the inscribed angle = the intercepted arc.
  3. The inscribed angle = half the sum of intercepted arcs.
  4. The size of the vertex angle outside the circle = 1/2 × (difference of intercepted arcs)

How many degrees is the central angle of an eighth of a circle?

45°

Is the vertex of the central angle is the center of the circle?

Central Angle and Arc Length The central angle of a circle is the angle based at the circle’s center. In other words, the vertex of the angle must be at the center of the circle.

How do you describe inscribed angle and central angle?

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. A central angle is any angle whose vertex is located at the center of a circle.

What is the main difference between a central angle and an inscribed angle?

An inscribed angle is an angle whose vertex lies on a circle, and its two sides are chords of the same circle. On the other hand, a central angle is an angle whose vertex lies at the center of a circle, and its two radii are the sides of the angle.

How did you determine the measure of the inscribed angles?

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.

What kind of angle is the central angle of a major arc?

A semi-circle is associated with half of a rotation which is 180°. Minor arcs are associated with less than half of a rotation, so minor arcs are associated with angles less than 180°. Major arcs are associated with more than half of a rotation, so major arcs are associated with angles greated than 180°.

What is the relationship between an angle and its arc?

The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That’s why radians are natural: a central angle of one radian will span an arc exactly one radius long.