Math Review: Pointers on Chords, Arcs, and Angles

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10 Questions

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

What is the formula to find the measure of an angle intersecting a chord?

Angle = ½(big arc + small arc)

What is the formula for finding the distance between a chord and a tangent?

(Chord)(Tangent) ÷ (Chord)² + (Tangent)²

What is the relationship between the measure of an angle intersecting a secant and the big and small arcs?

Angle = 2(big arc - small arc)

Which concept states that the tangent to a circle is perpendicular to the radius at the point of tangency?

Two Tangent Theorem

What is the measure of an angle intersecting a chord?

$\frac{1}{2}(\text{big arc} + \text{small arc})$

What is the formula for finding the distance between a chord and a tangent?

$(\text{chord} \times \text{tangent}) \div (\text{chord}^2 + \text{tangent}^2)$

Which theorem relates to congruent two tangents to a circle?

Two tangent theorem

What does the measure of an angle intersecting a secant depend on?

Difference between big and small arcs

What concept states that the tangent to a circle is perpendicular to what at the point of tangency?

Chord

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)

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.

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