12.3 inscribed angles

12.3 INSCRIBED ANGLESBrett Solberg AHS ‘11-’12

WARM-UP

1) What is the measure of arc AC?

2) What is the arc length of arc AC?

3)

Get out your notes and HW.

HW REVIEW

#8

TODAY’S AGENDA

Quiz 12.3 Inscribed Angles

Last day for retakes

QUIZ

3 Problems 6 minutes Use your notes Flip over when done

1) Is BC tangent to circle a? How do you know?

2) What is the perimeter of the polygon?

3) Find the value of x.

REVIEW

What is the difference between: arc length measure of an arc

Measure of an arc = measure of the central angle.

INSCRIBED CIRCLE

Inscribed Angle Angle whose vertex is on a circle and whose

sides are chords. Intercepted arc

Arc created by an inscribed angle.

EXAMPLE 1

Identify the inscribed angle and the intercepted arc.

THEOREM 12.9-INSCRIBED ANGLE THEOREM

The measure of an inscribed angle is half the measure of its intercepted arc.

ABC = ½AC

DEMONSTRATION

EXAMPLE 2

Find the measure of arc AC

EXAMPLE 2

Find the measure of arc PT and angle R.

EXAMPLE 2

Find the measure of angle G and angle D.

COROLLARIES TO THE INSCRIBED ANGLE THEOREM

1) Two inscribed angles that share an intercepted arc are congruent.

2) An angle inscribed by a semicircle is a right angle.

COROLLARIES TO THE INSCRIBED ANGLE THEOREM

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

angle N + angle O = 180˚ angle P + angle M = 180˚

THEOREM 12.10

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

EXAMPLE 4

RS and TU are diameters of circle A. RB is tangent to circle A at point R. Find the measure of angle BRT and TRS.

ASSIGNMENT

Worksheet 2.3

EC Assignment Due on THU pg. 711 #1 – 43 all