Podcast
Questions and Answers
What is the relationship between the measure of an inscribed angle and its intercepted arc?
What is the relationship between the measure of an inscribed angle and its intercepted arc?
- The measure of the inscribed angle is half the measure of the intercepted arc. (correct)
- The measure of the inscribed angle is double the measure of the intercepted arc.
- The measure of the inscribed angle is independent of the intercepted arc.
- The measure of the inscribed angle is equal to the measure of the intercepted arc.
If two inscribed angles intercept the same arc, what can be concluded about these angles?
If two inscribed angles intercept the same arc, what can be concluded about these angles?
- They are complementary.
- One angle measures twice as much as the other.
- They are always supplementary.
- They are congruent. (correct)
How is the measure of an angle formed by a tangent and a chord determined?
How is the measure of an angle formed by a tangent and a chord determined?
- It is half the measure of the intercepted arc. (correct)
- It is half the sum of the measures of the intercepted arcs.
- It is equal to the measure of the intercepted arc.
- It is equal to the sum of the measures of the intercepted arcs.
What does the secant-secant segment theorem state?
What does the secant-secant segment theorem state?
What is the correct equation according to the tangent-secant segment theorem?
What is the correct equation according to the tangent-secant segment theorem?
What is the measure of an inscribed angle if the measure of its intercepted arc is 80 degrees?
What is the measure of an inscribed angle if the measure of its intercepted arc is 80 degrees?
If a secant intersects a circle at points A and B, and a tangent intersects the circle at point C, what is the measure of the angle formed by the tangent and secant?
If a secant intersects a circle at points A and B, and a tangent intersects the circle at point C, what is the measure of the angle formed by the tangent and secant?
When two inscribed angles intercept the same arc, what can be concluded about their measures?
When two inscribed angles intercept the same arc, what can be concluded about their measures?
Which statement correctly describes an intercepted arc?
Which statement correctly describes an intercepted arc?
What happens to the measure of an inscribed angle when it intercepts a semicircle?
What happens to the measure of an inscribed angle when it intercepts a semicircle?
What is the relationship between the measures of the intercepted arcs when two secants intersect outside a circle?
What is the relationship between the measures of the intercepted arcs when two secants intersect outside a circle?
Flashcards
Inscribed Angle
Inscribed Angle
An angle formed by two chords that share an endpoint.
Intercepted Arc
Intercepted Arc
The arc on the inside of an inscribed angle, with endpoints on the angle.
Inscribed Angle Theorem
Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
Tangent
Tangent
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Tangent-Chord Angle Theorem
Tangent-Chord Angle Theorem
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Study Notes
Inscribed Angle and Intercepted Arcs
- An inscribed angle is an angle formed by two chords that share an endpoint.
- The intercepted arc is the arc that lies on the inside of the inscribed angle and has endpoints on the angle.
- The measure of an inscribed angle is half the measure of its intercepted arc.
- If two inscribed angles intercept the same arc, then the angles are congruent.
- If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Angles Formed by Tangent and Secant
- A tangent is a line that intersects a circle at exactly one point.
- A secant is a line that intersects a circle at exactly two points.
- The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
- 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 half the difference of the measures of the intercepted arcs.
Segments Formed by Secants and Tangents
- The secant-secant segment theorem states that if two secants are drawn from a point outside a circle, then the product of the external segment and the entire secant is equal to the product of the external segment and the entire secant. (This is a repeated statement, missing critical detail)
- The tangent-secant segment theorem states that if a tangent and a secant are drawn from a point outside a circle, then the square of the tangent segment is equal to the product of the external segment and the entire secant.
- These theorems provide relationships between lengths of segments formed by intersecting lines and circles.
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