Ch 11 mini Unit

LearningTarget 11-1 Tangents

• I can use tangents to a circle to find missing values in figures.

• A Tangent to a Circle is a line in the plane of a circle that intersects the circle in exactly one point. This point is called the point of tangency.

• If a line is tangent to a circle, then the line is perpendicular to the radius drawn at the point of tangency

• This gives us a Right triangle, soWe need to recallRight triangle properties

Find x

Find x

Find x

Find x

Find x

Inscribed or Circumscribed

• Do you remember the difference?

• Two points tangent to a circle from a point outside the circle are congruent

• Find the perimeter of the triangle

• Find the perimeter

• Homework p.586 #1-19 odd skip 5

Warmup p.589

Learning Target 11-2/11-3

• You will be able to use properties of chords to find missing values

• You will be able to use the Inscribed Angle Theorem to find missing angles and arcs

• Chord – a segment whose endpoints are on a circle

• Within a circle or in congruent circles–Congruent central angles have congruent

chords–Congruent Chords have congruent arcs–Congruent arcs have congruent central

angles

• Within a circle,–Chords equidistant from the center are

congruent–Congruent chords are equidistant from

the center

Find x

More properties of chords

• In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs• The reverse (converse) of this is true

also

• The measure of an inscribed angle is half the measure of its intercepted arc.• Pic/example

Properties of Inscribed Angles

• Two inscribed angles that intercept the same arc are congruent

• An angle inscribed in a semicircle is a right angle

• The opposite angles of a quadrilateral inscribed in a circle are supplementary.

• Examples p. 600

• The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.• Pic/example

Homework

• P.593-594 #3-19 odd skip 9• P. 601 1-19 odd

• WARMUPp. 605 Checkpoint QUIZ

Learning Target 11-4

• I can find measures of angles formed by chords, secants, and tangents.

• A secant is a line that intersects a circle at two points.

• We are going to use secants, tangents, and chords to solve problems See p.607

• Rules on page 609

Learning target 11-5

• I can write the equation of a circle

• An equation of a circle in a coordinate plane• +

• (h,k) is the center, and r is the radius

• Identify the center and the radius

• Graph

• Review• P.700 1-19, 21-23• P.627 6,7,89-12, 13-15, 16-21