Lesson 6.1 Properties of Tangents Page 182

Q1 Select A A.) This is the correct answer. B.) This is the wrong answer. C.) This is just as wrong as B

Q2 This time select B A.) This is the wrong choice. B.) This is the correct choice. C.) Do not select this answer.

Circle A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.

Radius A radius is a segment whose endpoints are the center and any point on the circle.

Chord A chord is a segment whose endpoints are on a circle. What is special about this one? A diameter is a chord that contains the center of the circle.

Secant Tangent A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency.

Q3 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P. A.) radius B.) chord C.) diameter D.) secant E.) tangent

Q4 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P. A.) radius B.) chord C.) diameter D.) secant E.) tangent

Q5 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P. A.) radius B.) chord C.) diameter D.) secant E.) tangent

Q6 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P. A.) radius B.) chord C.) diameter D.) secant E.) tangent

Q7 How many common tangents are possible between the two circles? A.) 1 B.) 2 C.) 3 D.) 4 E.) 5

Q8 How many common tangents are possible between the two circles? A.) 1 B.) 2 C.) 3 D.) 4 E.) 5

Q9 How many common tangents are possible between the two circles? A.) 1 B.) 2 C.) 3 D.) 4 E.) 5

Theorem 6.1: In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.

Theorem 6.2: Tangent segments from a common external point are congruent.

If we show that angle ABC is 90⁰ then segment BC must be a tangent. So angle ABC is 90⁰ and the segment BC is perpendicular to radius AB.

Example 5

Q10 What is the value of r? A.) 1 cm B.) 2 cm C.) 3 cm D.) 4 cm E.) 5 cm

Homework 1-22 page 186

Use the diagram to determine if the statement is true or false.

Hint