# How do you find the measure of an angle formed by a tangent and secant?

## How do you find the measure of an angle formed by a tangent and secant?

A secant is a line that intersects a circle in exactly two points. 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 measure of an angle formed by the tangent and a chord intersecting at the point of tangency?

Theorem 76: The measure of an angle formed by a tangent and a chord meeting at the point of tangency is half the measure of the intercepted arc.

### How do you find the measure of an angle that is tangent to a circle?

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.

Can a chord be a tangent?

Tangent: A tangent to a circle is a line, ray, or segment that touches the outside of the circle in exactly one point. It never crosses into the circle. A tangent can’t be a chord, because a chord touches a circle in two points, crossing through the inside of the circle.

## What is the angle between a tangent and a chord?

In any circle, the angle between a chord and a tangent through one of the endpoints of the chord is equal to the angle in the alternate segment, i.e. the angle subtended by the chord in the opposite side of the previous angle.

What can you say about the measure of the two intersecting tangents?

If two tangents intersect at a common point, then the measure of the angle formed is equal to half the difference of the measures of the intercepted arcs. The two intercepted arcs together create the whole circle. One arc is always a major arc with measure greater than 180°.

### What is the measure of XYZ?

Answer Expert Verified Angle subtended by an arc at the centre is twice of the angle subtended at any point on the circle . And in the given diagram, angle subtended on the circle by arc XZ=60 degree . So arc XZ =2*60=120.

Is the line tangent to the circle?

A tangent line is a line that intersects a circle at one point. Such a line is said to be tangent to that circle. The point at which the circle and the line intersect is the point of tangency. This means that for any tangent line, there exists a perpendicular radius.

## What type of angle is formed by a tangent line to a circle?

When a radius is drawn to a point of tangency, the angle formed is always a right (90 degree) angle. This fact is commonly applied in problems with two tangent segments drawn to a circle from a point.

How do you find the angle of a chord and a tangent?

An angle formed by a chord (link) and a tangent (link) that intersect on a circle is half the measure of the intercepted arc. Note: Like inscribed angles, when the vertex is on the circle itself, the angle formed is half the measure of the intercepted arc.

### Which is the measure of the intercepted arc?

The measure of the angle is equal to half the sum of the intercepted arcs. The angle x is equal to half the sum of the intercepted arcs. The intercepted arc a is the arc from C to D. The intercepted arc b is the arc from A to B.

What are the rules for finding angle and arc measures?

There are specific rules for finding angle and arc measures, depending on where the angles are drawn and the lines used to draw them. The lines create intercepted arcs, which are the arcs formed by chords, tangents, or secants. In this image, AB is the intercepted arc because it’s intercepted by chords AC and CB.

## Which is the intercepted arc of a chord?

The lines create intercepted arcs, which are the arcs formed by chords, tangents, or secants. In this image, AB is the intercepted arc because it’s intercepted by chords AC and CB. Angles that are formed inside of a circle by two chords create four arcs on a circle, which you can see in this diagram.

What is the measure of angle formed by a chord and tangent?

Chord A C intercepts a tangent tangent at point C. If the measure of a b c ⏜ = 70 ∘ , what is x? Use the theorem above to find the measure of angle formed by the intersection of the tangent that intersects chord AC . By the theorem, the measure of angle is half of the intercepted arc which is 70 ∘ .