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The measure of the angle formed by two secants intersecting outside the circle is one-half the difference of the intercepted arcs.

Example:

Major intercepted arc is 200o and the minor intercepted arc is 120o.

1/2 (200-120) = 40o ...

The measurement of the angle formed by the two secants is 40o.

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Related Questions

The measure of an angle formed by two secants intersecting inside the circle equals?

½ the sum of the intercepted arcs.


What is the measure of an angle formed by two secants intersecting outside the circle equals?

It is half the difference of the intercepted arcs.Suppose you have a circle with centre O and the two secants AB and CD, when extended meet at X which lies outside the circle.Then the two arcs subtended by the secants are AC and BD. These give the two angles as AOC and BOD and then the required angle is 0.5*(angle AOC - angle BOD).


What are secants?

Secants are lines that have a chord within them, and a chord is a segment that has endpoints on the circle itself.


What quadrant of the unit circle has negative secants?

Quadrants 2 and 3.


When segments intersect outside a circle what is the relationship between the angle of intersection and the intercepted arcs?

When two segments intersect outside a circle, the measure of the angle formed by the intersecting segments is equal to half the difference of the measures of the intercepted arcs. Specifically, if the angle is formed by segments that intersect outside the circle, the angle's measure is calculated as (Arc 1 - Arc 2)/2, where Arc 1 and Arc 2 are the measures of the arcs intercepted by the angle on the circle. This relationship helps in solving various geometric problems involving circles and angles.


How do you find angle measure in a circle?

To find an angle measure in a circle, you can use the relationship between the angle and the arcs it intercepts. For example, the measure of a central angle is equal to the measure of the arc it intercepts. For an inscribed angle, its measure is half of the measure of the intercepted arc. Additionally, you can apply the properties of angles formed by tangents, secants, and chords to determine angle measures.


A circle with no segment intersecting it?

no


Are all secants chords?

No, not all secants are chords. A secant is a line that intersects a circle at two points, while a chord is a segment whose endpoints lie on the circle. Therefore, while every chord can be considered a part of a secant line, not all secants are confined to just the segment between the two intersection points; they extend infinitely in both directions.


Why can't a circle have parallel or intersecting lines?

A circle cannot have parallel or intersecting lines because it is defined as the set of all points equidistant from a central point, resulting in a continuous curve. Any line drawn within or around a circle will either intersect the circle at two points (if it is a secant line), touch it at one point (if it is a tangent), or not intersect it at all (if it is outside the circle). Parallel lines, by definition, never meet, and since a circle is a closed curve, they cannot exist without intersecting at some point or being tangent. Thus, the nature of a circle inherently precludes the existence of parallel or intersecting lines within its geometric structure.


What is the measure of the angle formed by 2 chords intersecting within a circle if the opposite arcs they intercept are 90 and 130?

15pi. after you add.


What is an arc part of?

Arcs are part of a circumference of a circle cut into pieces by chords, tangents, secants, etc.


What happens to a chord when it leaves a circle?

It becomes a line intersecting the circle.