geometry B Unit 7 - all lessons
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
Given: AB¯ is tangent to ⊙C at B Find: x
14 m
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. ≅
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
6) Find the area of the sector of the circle.
200π
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
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
18) Name the part of the circle.
ABC
11) _____ are two arcs that intersect at exactly one point.
Adjacent arcs
17) Name the part of the circle.
BAC
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
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
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 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
Are the circles tangent, concentric, or congruent?
congruent
Congruent, concentric, or tangent? _____
congruent
4) Identify as a diameter, radius, chord, secant, or tangent.
diameter
A semicircle is an arc whose endpoints lie on a(n) _____.
diameter
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
4) The ______ arc is an arc formed by two lines or line segments that intersect a circle.
intercepted
Adjacent arcs are two arcs that _____ at exactly one point.
intersect
Identify the radius of the circle.
line AF
Identify a chord.
line DE
Identify the diameter of the circle.
line DE
Identify a tangent.
line m
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
2.017) indicates the _____
minor arc
A chord is a segment whose endpoints both lie _____ a circle.
on
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
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 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
8) The measure of an arc, which is equal to the measure of its central angle is called the _____.
semicircle
13) The point of _____ is the point where a tangent and a circle intersect.
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
A secant is a line that intersects a circle at _____ points.
two
14) Name the part of the circle.
⊙P
