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?
- Tangent-Secant Theorem (correct)
- Two Tangent Theorem
- Distance Formula Theorem
- External Point of Secant Theorem
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?
- Angle = 2(big arc - small arc)
- Angle = ½(big arc + small arc) (correct)
- Angle = big arc - small arc
- Angle = small arc - big arc
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?
- (Tangent) - (Chord)
- (Chord)(Tangent) ÷ (Chord)² - (Tangent)²
- (Tangent)² - (Chord)²
- (Chord)(Tangent) ÷ (Chord)² + (Tangent)² (correct)
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?
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?
What is the measure of an angle intersecting a chord?
What is 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?
Which theorem relates to congruent two tangents to a circle?
Which theorem relates to congruent two tangents to a circle?
What does the measure of an angle intersecting a secant depend on?
What does the measure of an angle intersecting a secant depend on?
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?
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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)
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