Aim #5: What theorems are related to arcs and chords in a circle (day 2)? Do Now: 1) Find the measure of x and y:

CC Geometry H

y

x E

32o

76o

2) is tangent to circle O. Find the measure of ≮BCD.

3) Tangents PA and PB are drawn to circle O from an external point P, and radii OA and OB are drawn. If m≮APB = 40, what is the measure of m≮AOB? Draw a picture.

Theorem: A diameter perpendicular to a chord bisects the chord and its arcs.

A B

D

O

C

 ≅

Corollary: The perpendicular bisector of a chord of a circle passes through the center of the circle.

A B

D

O

C

 ≅  ≅

Solve for the indicated variable(s).

110

x

O

1.2x­30 x

yz

O

xO

61

120 O

25x

 7

5. Find the length of a chord 3 inches from the center of a circle whose radius measures 5 inches.

6. In a circle of radius 10, mAB = 90o.

b) Find the distance from AB to the center of the circle, in radical form.

10 BC

a) Find the length of chord AB in radical form and to the nearest hundredth.

2.

3. 4.

7. In circle A, the radius is 14 and CD = 22. Find the measure of CE and EB. If necessary, leave your answer in simplest radical form.

o

o(           )

Theorem: If two chords of a circle are congruent, they are equidistant from the center of the circle. A

B

O

D

E

F

Theorem (Converse): If two chords are equidistant from the center of a circle, they are congruent.

c7 7

3

3 xx

2) Find x: 3) Find BD:

4) Find x and y: 5) Find BC:

1) Find x:

6) AB ≅ CD, OF = 16, CF = y + 10, and CD = 4y - 20. Find the length of DF and OA.

C

3x­50  x­10

2y­7 20

x+502x­10

3y­7 20

Name_________________________ CC Geometry H Date ___________________ HW #5

1) OC = 5cm AB = 8cm. Find OP. 2) Find x and y:

3) Find the length of BD:

5) OA = 6, OE = 2. Find CE in simplest radical form.

6) DB = 34, AC = 30. Find the length of BE.

Solve for the variable(s).

4) Find x and y:

(        )o (          )o

(          )o (         )o

Review1) Write the equation of the line that is the perpendicular bisector of segment AB if A(4, -7) and B(8, 3).

2) If the side of a square is (x + 3), then express the diagonal of the square in terms of (x + 3).

>

>

(2x)0

(5x ­ 51)0

3) Find the measure, in degrees, of ≮BHE. Justify your answer.

4) The diagram shows the dimensions of a concrete cylinder. Concrete has a density of 2.3 grams per cubic centimeter. Find the mass of the concrete cylinder to the nearest gram.

1.2 m

.7m

5) A ship is at position A on the sea surface and locates a wreck, C, on the seabed 321 m vertically below. The ship then steams 525 m due west until it reaches position B. From its new position at B, what is the measure of the angle of depression from B to the wreck C, to the nearest degree?

321 m

525 m