Podcast
Questions and Answers
Which theorem states that the measure of angle intersecting a secant is half the difference between the big arc and the small arc?
Which theorem states that the measure of angle intersecting a secant is half the difference between the big arc and the small arc?
What is the formula to find the measure of an angle intersecting a chord?
What is the formula to find the measure of an angle intersecting a chord?
What is the formula for finding the distance between a chord and a tangent?
What is the formula for finding the distance between a chord and a tangent?
What is the relationship between the measure of an angle intersecting a secant and the big and small arcs?
What is the relationship between the measure of an angle intersecting a secant and the big and small arcs?
Signup and view all the answers
Which concept states that the tangent to a circle is perpendicular to the radius at the point of tangency?
Which concept states that the tangent to a circle is perpendicular to the radius at the point of tangency?
Signup and view all the answers
What is the measure of an angle intersecting a chord?
What is the measure of an angle intersecting a chord?
Signup and view all the answers
What is the formula for finding the distance between a chord and a tangent?
What is the formula for finding the distance between a chord and a tangent?
Signup and view all the answers
Which theorem relates to congruent two tangents to a circle?
Which theorem relates to congruent two tangents to a circle?
Signup and view all the answers
What does the measure of an angle intersecting a secant depend on?
What does the measure of an angle intersecting a secant depend on?
Signup and view all the answers
What concept states that the tangent to a circle is perpendicular to what at the point of tangency?
What concept states that the tangent to a circle is perpendicular to what at the point of tangency?
Signup and view all the answers
Study Notes
Circles and Angles
- A chord is a line segment within a circle, having both endpoints on the circle.
- An arc is a part of a circle, bounded by two endpoints (called vertices).
- A central angle is an angle whose vertex is the center of a circle.
- An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle.
Tangents and Secants
- A tangent is a line that intersects a circle at exactly one point (called the point of tangency).
- A secant is a line that intersects a circle at two or more points.
Two Tangent Theorem
- If two tangent lines intersect at an external point, then the tangent segments to the circle from that point are congruent.
Tangent-Secant Theorem
- (Tangent) = (Secant) × (external point of secant)
Distance Formula
- The distance between two points (x₁, y₁) and (x₂, y₂) is given by: √((x₂ - x₁)² + (y₂ - y₁)²)
Measure of Angles
- Measure of an angle intersecting a chord: Angle = ½(big arc + small arc)
- Measure of an angle intersecting a secant: Angle = ½(big arc - small arc)
Finding the Distance
- The distance from the center of a circle to a point outside the circle is given by: (chord)(tangent) ÷ √((chord)² + (tangent)²)
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Prepare for your math exam by reviewing essential concepts such as chords, arcs, central and inscribed angles, as well as tangents and secants. This comprehensive review covers the two tangent theorem, congruent two tangent theorem, measures of intersecting angles, and more.
