geometry B Unit 7 - all lessons

Given: AB¯ is tangent to ⊙C at B Find: x

14 m

Identify the center of the circle.

A

11) Identify the part of the circle:

A= circumference B= center c= radius D= diameter

15) Name the part of the circle.

ABC

17) Name the part of the circle.

BAC

4) A(n) _____ angle is an angle whose vertex is a point on a circle and whose sides are two chords of the circle.

inscribed

Identify a tangent.

line m

A chord is a segment whose endpoints both lie _____ a circle.

on

22) Choose the correct standard form equation from the information given. Center (-4,2) radius 7

(x+(-4))2+(y-2)2=72 (x-4)2+(y-2)2=49

24) Choose the correct standard form equation from the information given. Center (2,0) radius 3

(x+(-5))2+(y+(-7))2=102 (x-5)2+(y-7)2=100

20) Choose the standard form equation of the circle below.

(x+1)2-(y+3)2=42 (x+1)2-(y+3)2=16

21) Choose the standard from equation of the circle below.

(x-0)2-(y+0)2=32 x2+y2=9

24) Choose the correct standard form equation from the information given. Center (2,0) radius

(x-2)2+(y+0)2=32 (x-2)2+y2=6

23) Choose the correct standard form equation from the information given. Center (5,7) radius 10

(x-5)2+(y-7)2=102 (x-5)2+(y-7)2=20

13) Given: Inscribed ∠ABC intercepts semicircle ADC⌢

1. semicircle 2. through any two points there is exactly on line 3. def of right angle 4.def of right angle 5. def of angle 6. def of angle

Find the length of the arc.

12 ft

15) Using binoculars, a lighthouse operator was scanning the ocean from the observation deck which is 132 feet off the ground. He observed that a shop just on the horizon was in distress. He quickly notified the Coast Guard of the ship's condition and position. How far away from the lighthouse, to the nearest whole mile, was the ship. Use the Pythagorean Theorem. Convert the height of the lighthouse to miles. 5280 feet = 1 mile.

14 miles

9) Find the length of the arc on the circle. Use π=3.14

14m

3) Given: ⊙P with radii PQ¯and PR¯; PQ¯⊥AC¯; PR¯⊥DF¯; BP¯≅EP¯

2. a. Through any two points there is exactly one line. 4. e. CPCTC 6. bisector 9. k ⊥ lines 15. g. Addition Prop. of = 17. j. ≅

3) Given: Quadrilateral ABCD is inscribed in ⊙P

2. angle 3. inscribed angle 4. angle 6. symmetric 7. add. prop. of

1) Given: ∠APB≅∠CPD

2. d. CD¯ 3. a. SAS

20) Given: AB⌢≅CD⌢

2. d. congruent arcs 3. f. m∠APB=m∠CPD 4. e. congruent angles

19) Given: AB¯≅CD¯

2. h. SAS 3. c. ΔACP≅ΔBDP 5. g. congruent ∠s 7. d. congruent segments

1) Given: ⊙S with two secants, MO→ and NP→ that intersect in the interior of the circle at Q Prove: m∠MQP=12(mMP⌢+mNO⌢)

2. isosceles triangle 3. pythagorean 4. addition 6. pythagorean 7. addition

2) Given: ⊙P with ∠EDG inscribed with P in the interior of ∠EDG

2. through any two points there is exactly on line 4. angle 8. add. prop. of 9. arc

12) Given: ⊙P with ∠HGI inscribed with P in the exterior of ∠HGI

2. through any two points there is exactly on line 4. subtr. prop. of 5. subtr. prop. of 7. subst. 9. circle 11. arc

6) Find the area of the sector of the circle.

200π

Find the area of the sector.

225

Find the area of the segment. The area of the sector is 37.7 in2 and the area of the triangle is 13 in2.

24.7 in2

Find the area of the triangle.

24.7 in2

14) Find the height of the tower in feet. Use the Pythagorean Theorem. Convert the height of the mountain to miles first. There are 5,280 feet in a mile.

264 ft

1) Given: EG¯and FG¯are tangents to ⊙P

3. d,j 4. e 5. e, i 6. g 8.f d. EP¯ e. PFG f. Reflexive Property of ≅ g. angle i. ≅ j. FP¯

2) Given: AB¯⊥CD¯

3. f. Reflexive Property of ≅ 4. c. right Δs 6. c. right Δs 7. d. ⊥ 8. i. Transitive Property of ≅

5) Find the area of the sector of the circle.

300π

18) Use π=3.14.

31.4 cm

19) Solve. Use π=3.14.

31.4 cm2

Find the area of the sector.

37.7 in2

1) Given: ⊙P with inscribed ∠BAC

4. add 5. sud 6. equal 7. segment 9. add

Find the area of the sector.

40pi mm2

18) Name the part of the circle.

ABC

11) _____ are two arcs that intersect at exactly one point.

Adjacent arcs

16) Name the part of the circle.

BC

10) _____ circles are coplanar circles that share a common center.

Concentric

13) _____ are arcs that have the same measure within the same circle or congruent circles.

Congruent arcs

Identify a secant.

GE line

Identify the circumference of the circle.

J

16) Why is it important to state that a tangent must be in the same plane as a circle?

Otherwise, there would be many tangent lines that would intersect the circle in the same point.

2) _____ is a mathematical constant that is equal to the ratio of the circumference of a circle to its diameter.

Pi

8) Find the indicated areas. Use π=3.14

Sector area: 62.8 square feet Triangle area: 48 square feet Segment area: 14.8

7) Find the indicated areas. Use π=3.14

Sector area:8.8 square feet Triangle area: 15.6 square feet Segment area: 3.2 square feet

12) The measure of an arc formed by two adjacent arcs is the _____ of the measures of the two arcs. (Arc Addition Postulate)

adjacent arcs

3) The measure of the distance along an arc measured in linear units is the _______ length.

arc

6) A(n) _____ is a continuous portion of a circle consisting of two endpoints and all the points on the circle between them.

arc

A(n) _____ is a continuous portion of a circle consisting of two endpoints and all the points on the circle between them.

arc

3) The point in the interior of the circle that is equidistant from every point on the circle is called the _____ of the circle.

center

A radius of a circle is a segment whose endpoints are the _____ of the circle and a point on the circle.

center

An angle with its vertex at the _____ of a circle is called the central angle.

center

The arc measure is equal to the measure of its _____ angle.

central

2.013) indicates the _____

central angle

7) An angle with its vertex at the center of a circle is called the _____.

central angle

3) Identify as a diameter, radius, chord, secant, or tangent.

chord

9) A _____ is a segment whose endpoints both lie on the circle.

chord

1) A _____ is the locus of points in a plane that are all equidistant from a single point.

circle

4) The measure of a(n) _____ in degrees is 360º.

circle

The circumference is the distance around a _____.

circle

7) The _____ is the distance around the circle.

circumference

Are the circles tangent, concentric, or congruent?

concentric

Congruent, concentric, or tangent? _____

concentric

10) If inscribed angles in a circle or congruent circles intercept the same arc or congruent arcs, then the angles are _____.

congruent

10) If two segments are tangent to a circle from the same point in the exterior of the circle, then the segments are _____. (Theorem 7.2C)

congruent

5) All radii on the same circle are _____. (Theorem 7.1A)

congruent

8) Circles that have congruent radii are _____.

congruent

Arcs that have the same measure within the same circle or congruent circles are called _____ arcs.

congruent

Are the circles tangent, concentric, or congruent?

congruent

Congruent, concentric, or tangent? _____

congruent

1. If inscribed angles in a circle or congruent circles intercept the same arc or congruent arcs, then the angles are _____. (Theorem 7.5B) 2. The measure of an inscribed angle is _____ the measure of its intercepted arc. (Inscribed Angle Theorem) 3. If a quadrilateral is inscribed in a circle, then its _____ angles are supplementary. (Theorem 7.5D) 4. If a tangent and a secant intersect a circle at the point of tangency, then the measure of the angle formed is half the measure of the _____ arc. (Theorem 7.6A) 5. If a tangent and a secant, two tangents, or two secants intersect in the _____ of a circle, then the measure of the angle formed is half the difference of the measures of the intercepted arcs. (Theorem 7.6C) 6. If two secants intersect in the _____ of a circle, then the measure of each angle formed is half the sum of the measures of the intercepted arcs. (Theorem 7.6B) 7. A(n) _____ angle is an angle whose vertex is a point on the circle and whose sides are two chords of the 8. Given: Inscribed angles, ∠DAC and ∠CBD Prove: ∠DAC≅∠CBD 9. If an inscribed angle intercepts a(n) _____ then the angle is a right angle. (Theorem 7.5C)

congruent half opposite intercepted exterior interior inscribed 2. inscribed angle 3. equal 4. congruent angles semicircle

4) Identify as a diameter, radius, chord, secant, or tangent.

diameter

5) The measure of an inscribed angle whose side is a _____ is half the measure of its intercepted arc. (Corollary 1 of the Inscribed Angle Theorem)

diameter

A semicircle is an arc whose endpoints lie on a(n) _____.

diameter

4) If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the _____ of the measures of the intercepted arcs. (Theorem 7.6C)

difference

A circle is a locus of points in a plane that are _____ from a single point.

equidistant

The major arc is the set of points that lie on an arc in the _____ of the central angle of a circle.

exterior

6) The measure of an inscribed angle is _____ the measure of its intercepted arc.

half

11) The measure of an inscribed angle with the center of the circle in the interior of the angle is half the measure of its _____ arc. (Corollary 2 of the Inscribed Angle Theorem)

intercepted

4) The ______ arc is an arc formed by two lines or line segments that intersect a circle.

intercepted

9) The measure of an inscribed angle with the center of the circle in the exterior of the angle is half the measure of its _____ arc. (Corollary 3 of the Inscribed Angle Theorem)

intercepted

2.014) indicates the _____

intercepted arc

The minor arc is the set of points that lie on an arc in the _____ of the central angle of a circle.

interior

Adjacent arcs are two arcs that _____ at exactly one point.

intersect

8) Given: ⊙P with two secants, AC→ and AD→ that intersect in the exterior of the circle at A Prove: m∠CAD=12(mCD⌢-mBE⌢)

isosceles exterior through two points exterior pythagorean

Identify the radius of the circle.

line AF

Identify a chord.

line DE

Identify the diameter of the circle.

line DE

The arc length is the measure of the distance along an arc measured in _____ units.

linear

9) The _____ is the set of all points that lie on an arc in the exterior of a central angle.

major arc

The diameter of a circle is a segment that passes through the _____ of a circle and whose endpoints are on the circle.

midpoint

10) The _____ is the set of all points that lie on an arc in the interior of a central angle.

minor arc

2.015) indicates the _____

minor arc

2.017) indicates the _____

minor arc

A tangent is a line in the same plane as the circle that intersects the circle at exactly _____ point(s).

one

8) If a line is tangent to a circle, then it is _____ to the radius drawn from the point of tangency. (Theorem 7.2A)

perpendicular

12) If a line is perpendicular to a _____ of a circle at exactly one point on the circle, then the line is tangent to the circle. (Theorem 7.2B)

radius

6) Identify as a diameter, radius, chord, secant, or tangent.

radius

9) A _____ of a circle is a segment whose endpoints are the center of the circle and a point on the circle.

radius

5) Identify as a diameter, radius, chord, secant, or tangent.

secant

7) A _____ is a line that intersects a circle at two points.

secant

7) Identify the relationship between the intersecting line pairs and the circle.

secant-secant

6) Identify the relationship between the intersecting line pairs and the circle.

secant-tangent

1) A ______ of a circle is a region within a circle bounded by two radii and their intercepted arc.

sector

2.016) indicates the _____

sector

2.018) indicates the _____

sector

A(n) _____ of a circle is a region within a circle bounded by an arc and its chord.

sector

A(n) _____ of a circle is a region within a circle bounded by two radii and their intercepted arc.

sector

2) A _______ of a circle is a region within a circle bounded by an arc and its chord.

segment

2.019) indicates the _____

semicircle

5) A(n) _____ is an arc whose endpoints lie on a diameter of a circle.

semicircle

7) If an inscribed angle intercepts a _____, then the angle is a right angle. (Theorem 7.5C)

semicircle

8) The measure of an arc, which is equal to the measure of its central angle is called the _____.

semicircle

2) If two secants intersect in the interior of a circle, then the measure of each angle formed is half the _____ of the measures of the intercepted arcs. (Theorem 7.6B)

sum

8) If a quadrilateral is inscribed in a circle, then its opposite angles are _____. (Theorem 7.5D)

supplementary

13) The point of _____ is the point where a tangent and a circle intersect.

tangency

3) If a tangent and a secant intersect a circle at the point of _____, then the measure of the angle formed is half the measure of the intercepted arc. (Theorem 7.6A)

tangency

11) A line in the same plane as the circle that intersects the circle at exactly one point is called a _____.

tangent

2) Identify as a diameter, radius, chord, secant, or tangent.

tangent

4) The _____ of a circle is a segment that passes through the center of a circle and whose endpoints are on the circle.

tangent

6) Coplanar circles that intersect at exactly one point are called _____ circles.

tangent

Coplanar circles that intersect at exactly one point are called _____ circles.

tangent

The point of tangency is the point where a _____ and a circle intersect.

tangent

5) Identify the relationship between the intersecting line pairs and the circle.

tangent-tangent

A secant is a line that intersects a circle at _____ points.

two

The intercepted arc is an arc formed by _____ lines or line segments that intersect a circle.

two

14) Name the part of the circle.

⊙P