anglestangents secants & chords grab bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200...

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Page 1: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Page 2: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Angles Tangents Secants & Chords

Grab Bag

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Page 3: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

In the accompanying diagram of circle O, and . Find the value of x.

xABCm 260xACm

Page 4: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=20

Page 5: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given the circle below with diameter , find x. AB

Page 6: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=90°

Page 7: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given a circle with the center indicated, find x.

Page 8: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=40

Page 9: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

True or False: In the same circle, or

congruent circles, congruent central

angles have congruent arcs.

Page 10: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

True

Page 11: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given two secants shown in the diagram, find the number of degrees in the angle labeled x.

Page 12: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=60°

Page 13: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

In the diagram, the segments shown are tangent to the circle. Find the value of x.

Page 14: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=5

Page 15: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

In the diagram, tangent and secant are

drawn to circle O from point A, AB=6 and AC=4. Find AD.

AB ACD

Page 16: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

AD=9

Page 17: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

How many common tangents can be drawn for

two externally tangent circles?

Page 18: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

3 tangents

Page 19: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given tangent to the circle shown. Find the measure of the arc designated by x.

AC

Page 20: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

260

Page 21: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given the circle shown with two tangents to the circle from a common external point. Find the measure of

the angle marked x.

Page 22: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

80

Page 23: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given the circle in the diagram with two intersecting chords. Find the length x.

Page 24: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=8

Page 25: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

In the diagram, secant intersects circle O at D, secant intersects circle O at E, AE=4, AC=24 and AB=16. Find AD.

AB

AC

Page 26: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

AD=6

Page 27: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given a circle with two secants as shown in the diagram. Find the value of the arc designated by x.

Page 28: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=25

Page 29: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

In the given diagram of the circle below with radius 5. Find the length of the segment labeled x.

Page 30: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=4

Page 31: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given: Tangent , diameter , and secant in circle O. What two sets of congruent angles can be used to prove ?

AD

CD AC

DBCADC ~

Page 32: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

and 11 4ADC

Page 33: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given: Circle O with diameter , and . Find .

CD CDAB ||

80ABm

CAm

Page 34: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

50CAm

Page 35: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given the circle in the diagram with the indicated center. Find the measure of

the arc marked x.

Page 36: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

x=55

Page 37: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Given: in circle O. Which method can be used to prove that ?

ACAB

ABOACO

Page 38: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

SSS Postulate

SAS Postulate ASA Postulate

Page 39: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

A cathedral window is built in the shape of a semi circle. If the window is to contain 3 stained glass sections of equal size, what is the area of each section to the nearest square foot?

Page 40: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

3 ft2

Page 41: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

Two chords intersect within a circle to form an angle whose measure is 53°. If the intercepted arcs are given by 3x+3 and 10x-14, find the measure of the larger arc.

Page 42: AnglesTangents Secants & Chords Grab Bag 100 200 300 400 500 300 400 500 200 300 400 500 100 200 300 400 500

76°

200 300 400 500 Europe & Geography 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100

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