What is the relationship between a central angle and its arc?

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the center. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

What is the relationship between a central angle and its arc Quizizz?

What is the relationship between a central angle and its arc? The angle is half of the arc.

Is a central angle equal to its arc?

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What is the relation between central angle and inscribed angle standing on the same arc?

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

How do the central angle and the arc length of a circle relate to one another?

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.

What is the relationship between two tangents that share a common endpoint outside of the circle?

If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.

What can you conclude about the relationship between radii and tangents?

The radius of a circle is perpendicular to the tangent line through its endpoint on the circle’s circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line.

What relationship do the two segments that are tangent from the same circle to the same point have?

In other words, tangent segments drawn to the same circle from the same point (there are two for every circle) are equal.

What is the relationship of a second and a tangent intersecting in the exterior of a circle to its intercepted arcs?

related to the intercepted arcs. If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

What is the relationship of a second and a tangent intersecting?

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

What is the relationship of two S intersecting in the interior of a circle to the measures of the intercepted arcs and its vertical angle?

Angles of Intersecting Chords Theorem



If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

What is the relationship of two secants intersecting in the exterior?

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

When two secants intersect outside a circle the circle divides the secants into segments that are proportional with each other?

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other. Two Secants Segments Theorem: If two secants are drawn from a common point outside a circle and the segments are labeled as below, then a(a+b)=c(c+d).

What is the relationship among the segments formed inside a circle when two secants lines intersect in the interior of a circle?

1. Intersecting Chords Theorem. If two chords or secants intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

What is the relationship of two secants intersecting in the interior of a circle to the measures of the intercepted?

If two lines intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs . In the circle, the two lines ↔AC and ↔AE intersect outside the circle at the point A .

What is the relationship of two secants?

When two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

What have you learned about the relationship between secants and the measurement of the angles and arcs?

Theorem 9-13: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

What is the relationship between an angle formed by two secants two tangents or a secant and a tangent and its intercepted arcs?

When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

What is the relationship between an angle formed by two chords and its intercepted arcs?

If two chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.