Chapter 6 Circle Theorems And Puzzles

Question 1

Secant line

Answer 1

A segment that intersects the circle twice

Question 2

Tangent line

Answer 2

A line that intersects the circle only at one point

Question 3

Point of tangency

Answer 3

The point where the tangent line intersects the circle

Question 4

Semicircle Arc

Answer 4

1) Half the circle
2) 180°
3) Three letters to label ABC (with arc notation over them)

Question 5

Minor arc

Answer 5

1) Less than 180°

2) Two letters to label AB (with arc notation)

Question 6

Major arc

Answer 6

1) Greater than 180°

2) Use three letters to label ABC (with arc notation)

Question 7

Inscribed Angle

Answer 7

1) An angle with the vertex on the circle

2) The angle is half the arc measure

Question 8

Central angle

Answer 8

1) An angle with the vertex on the center

2) The angle is congruent to the arc measure

Question 9

Inscribed right triangle

Answer 9

The angle inscribed in a semicircle is a right angle

Question 10

Congruent chords

Answer 10

Congruent chords make congruent arcs

Question 11

Angle created by a tangent and a chord

Answer 11

1) The chord and tangent meet at the point of tangency

2) The chord/tangent angle it half the arc it subtends. (Cuts out)

Question 12

Perpendicular radius and chord

Answer 12

A radius is perpendicular to the chord and bisects the chord and the arc the chord subtends.

Question 13

Two arcs, chords, and radii

Answer 13

Chords that are the same distance from the center are congruent, along with their arcs and radii.

Question 14

Radius and tangent line

Answer 14

The radius is perpendicular to the tangent line at the point of tangency.

Question 15

Inscribed quadrilateral

Answer 15

Opposite angles are supplementary
\_\_\_\_\_\_\_\_\_\_\_\_
|180-x  180-y|
|                     |
|y                 x|
----------------

Question 16

Twin tangents

Answer 16

Tangent from the same point are congruent.

Question 17

Two chord lengths

Answer 17

ab=cd

Question 18

Two secants length

Answer 18

Outsidewhole thing=Outsidewhole thing (se=ca)

Question 19

1 tangent, 1 secant length

Answer 19

t^2= outsidewhole length
Or
t^2= se

Question 20

Smiley face (2 tangent, 2 radii)

Answer 20

The angle created by the two radii is the same as the arc created by the two tangents. The tangent angle is x, the arc and the central angle is 180-x.

Question 21

Circumference

Answer 21

C=2rPi
C=dPi
Pi=c/d (d is the number of times the circle)

Question 22

Arc length

Answer 22

A= x°/360°*2(Pi)r

Question 23

Chord

Answer 23

A segment with end points on the circle

Question 24

Two chords angle

Answer 24

Angle1=(k+j)/2

other format vanished, leaving just m for no reason.

Question 24

Two secants angle

Answer 24

Angle1=(k-j)/2

Question 24

1 tangent, 1 secant angle

Answer 24

Angle1=(k-j)/2

Question 24

2 tangents angle

Answer 24

Angle1=(k-j)/2