Ch 11 mini Unit. LearningTarget 11-1 Tangents I can use tangents to a circle to find missing values in figures.

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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, so We need to recall Right triangle properties

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

Identify the center and the radius

Graph

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

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