geometry B Unit 7 - all lessons

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

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

7) The _____ is the distance around the circle. : circumference

8) Circles that have congruent radii are _____. : congruent

Congruent, concentric, or tangent? _____ : congruent

Congruent, concentric, or tangent? _____ : concentric

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

23) Choose the correct standard form equation from the information given.Center(5,7)radius10 : (x-5)2+(y-7)2=102(x-5)2+(y-7)2=20

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

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

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

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

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

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.

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

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

Are the circles tangent, concentric, or congruent? : concentric

Are the circles tangent, concentric, or congruent? : congruent

The circumference is the distance around a _____. : circle

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

2) Given: AB¯⊥CD¯ : 3. f. Reflexive Property of ≅4. c. right Δs6. c. right Δs7. d. ⊥8. i. Transitive Property of ≅

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. CPCTC6. bisector9. k ⊥ lines15. g. Addition Prop. of =17. j. ≅

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

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

14) Name the part of the circle. : ⊙P

15) Name the part of the circle. : ABC

20) Given: AB⌢≅CD⌢ : 2. d. congruent arcs3. f. m∠APB=m∠CPD4. e. congruent angles

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

6) Find the area of the sector of the circle. : 200π

7) Find the indicated areas. Use π=3.14 : Sector area:8.8 square feetTriangle area: 15.6 square feetSegment area: 3.2 square feet

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

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

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

2.017) indicates the _____ : minor arc

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

2.015) indicates the _____ : minor arc

Find the length of the arc. : 12 ft

Find the area of the sector. : 225

1) Given: ⊙P with inscribed ∠BAC : 4. add5. sud6. equal7. segment9. add

2) Given: ⊙P with ∠EDG inscribed with P in the interior of ∠EDG : 2. through any two points there is exactly on line4. angle8. add. prop. of9. arc

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

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

13) Given: Inscribed ∠ABC intercepts semicircle ADC⌢ : 1. semicircle2. through any two points there is exactly on line3. def of right angle4.def of right angle5. def of angle6. def of angle

1) Given: ⊙S with two secants, MO→ and NP→ that intersect in the interior of the circle at QProve: m∠MQP=12(mMP⌢+mNO⌢) : 2. isosceles triangle3. pythagorean4. addition6. pythagorean7. addition

6) Identify the relationship between the intersecting line pairs and the circle. : secant-tangent

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