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Gemiola [76]
3 years ago
15

Which statements are true regarding the relationships between central, inscribed, and circumscribed angles of a circle? Check al

l that apply.
A circumscribed angle is created by two intersecting tangent segments.

A central angle is created by two intersecting chords that are not a diameter.

The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc.

The measure of a central angle will be half the measure of an inscribed angle that intercepts the same arc.

The measures of a central angle and circumscribed angle that intercept the same arc will sum to 90°.

The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle.

Mathematics
2 answers:
mamaluj [8]3 years ago
8 0

Answer:

# A circumscribed angle is created by two intersecting tangent segments ⇒ true (1st answer)

# The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc ⇒ true (3rd answer)

# The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle ⇒ true (6th answer)

Step-by-step explanation:

* Lets revise the types of angles in a circle

- A circumscribed angle is the angle made by two intersecting

 tangent lines to a circle (it's out side the circle)

- Its measure is half the difference of the measures of the two

 intercepted arcs

- Ex:

∵ AB and AC are tangent to circle M at B and C

∴ ∠A is a circumscribed angle

∴ m∠A = 1/2(m major arc BC - m minor arc BC)

- An inscribed angle is an angle formed by two chords in a circle

  which have a common endpoint, this common endpoint is the

  vertex of it

- Its measure is half the measure of the intercepted arc

Ex:

∵ XY and XZ are two chords in circle M

∴ ∠YXZ is an inscribed angle subtended by arc YZ

∴ m∠YXZ = 1/2 (m arc YZ)

- A central angle is an angle with endpoints located on the

 circumference of the circle and its vertex is the center of the circle

- Its measure is the measure of the intercepted arc

- Ex:

∵ MA and MB are two radii of circle M

∴ ∠AMB is a central angle subtended by the opposite arc AB

∴ m∠AMB = m of arc AB

- The measure of an inscribed angle is half the measure of the

  central angle which subtended by the same arc

- Ex:

∵ ∠ABC is an inscribed angle in circle M subtended by arc AC

∵ ∠AMC is a central angle subtended by arc AC

∴ m∠ABC = 1/2 m∠AMC

∴ m∠AMC = 2 m∠ABC

* Lets solve the problem

- From the facts above:

# A circumscribed angle is created by two intersecting tangent

  segments ⇒ true

# The measure of a central angle will be twice the measure of an

   inscribed angle that intercepts the same arc ⇒ true

- Lets prove the last statement

∵ AMC is a central angle of circle M subtended by arc AC

∴ m∠AMC = m of arc AC ⇒ (1)

∵ XYZ is an inscribed angle of circle M subtended by arc XZ

∴ m∠XYZ = 1/2 m of arc XZ

∵ m of arc XZ is twice m of arc AC

∴ m∠XYZ = m of arc AC ⇒ (2)

- From (1) and (2)

∴ m∠AMC = m∠XYZ

∴ The statement down is true

# The measure of a central angle will be equal to the measure of

   an inscribed angle when the arc intercepted by the inscribed

   angle is twice as large as the arc intercepted by the central

   angle ⇒ true

amm18123 years ago
3 0

Answer:

<h3>A circumscribed angle is created by two intersecting tangent segments.</h3><h3>The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc.</h3><h3>The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle.</h3>

Step-by-step explanation:

We can choose the correct answers by studying their definitions.

A circumscribed angle is defined by two tangent segments, which have an external common point, to their tangent point, as you can see in the image attached, thats why the first answer is correct.

The third answer belongs to a geometrical conjecture, which says:  <em>''In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc''. </em>This conjecture stablished a relation between a central angle and an inscribed angle. Textually, it says that the inscribed is half of the central, which is the same if we say, the central is twice the inscribed.

The last answer is a variation of the conjecture we used before. In this case, if the arc is twice, then inscribed and central are equal, this is deducted from that conjecture, only considering the opposite case, which angles are equal and arcs don't.

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What is the volume of the square pyramid with base edges 4 m and height 3 m
olya-2409 [2.1K]

16 m³

Step-by-step explanation:

Step 1:

Here we are going to find the volume of square pyramid.

Volume of square pyramid = (1/3) × (Base)^{2} × (Height)

Here base = 4 m

         Height = 3 m

Step 2:

Volume = (1/3) × (4 × 4) × 3

              = 16 m³

5 0
3 years ago
Jim and Jackie are married with three children at home and a mortgage. Jim’s net pay per year is $67,000 and Jackie does not hav
rodikova [14]

The correct option is that they should work on their plan for managing income.

<h3>How to illustrate the information?</h3>

Given that Jim and Jackie are married with three children and have a home at mortgage.

The net pay per year of Jim is $67,000 and Jackie do not earn at all. The mortgage expenses and monthly expenses are

$(2,800+2,700) = $5,500, not much as compared to the total income.

Also, Jim contributes 15% of his income , i.e., $10050 into the retirement fund and also they have savings of $5,000.

In addition, there is a $500,000 life insurance policy on Jim and a $100,000 policy on Jackie.

Therefore, looking at all of these, it can be concluded that the net income of Jim per year is not bad at all to manage the expenses, they just have to work on it little more to run the family smoothly.

Thus, the correct option is that they should work on their plan for managing income.

Learn more about income on:

brainly.com/question/25745683

#SPJ1

Complete question:

Jim and Jackie are married with three children at home and a mortgage. Jim’s net pay per year is $67,000 and Jackie does not have income. Their mortgage payment of $2,800 includes insurance on their home. They have additional monthly expenses of $2,700. Jim contributes 15% of his earnings to a retirement fund and they have $5,000 in savings. There is a $500,000 life insurance policy on Jim and a $100,000 policy on Jackie. As their financial advisor, what part of Jim and Jackie’s financial plan would you encourage them to work on? a. They should work on their plan for managing income. b. They should work on their plan for managing their liquidity. c. They should work on their plan for protecting their assets. d. They should work on their plan for protecting their income.

3 0
2 years ago
Please help! 25points! pleaseeee helppppp
BaLLatris [955]

Answer: this is difficult


Step-by-step explanation:


6 0
3 years ago
Adisa borrows $5,000 at 14% interest, compounded twice a year. How much does she owe at the end of 8 years?
N76 [4]

The borrower owes $14,760.82  at the end of 8 years

What is compounding interest?

Compounding interest means that earlier interest would earn more interest in the future alongside the loan principal.

Note that in this case the loan continues to accumulate interest because there no repayments, in other words, the loan balance after 8 years, which comprises of the principal and interest for 8 years can be computed using the future value formula of a single cash flow(the single cash flow is the principal) as shown thus:

FV=PV*(1+r/n)^(n*t)

FV=loan balance after 8 years=unknown

PV=loan amount=$5,000

r=annual interest=14%

n=number of times in a year that interest is compounded=2(twice a year)

t=loan period=8 years

FV=$5000*(1+14%/2)^(2*8)

FV=$5000*(1.07)^16

FV=$5000*2.95216374856541

FV=loan balance after 8 years=$14,760.82

Find out more about semiannual compounding on:brainly.com/question/7219541.

#SPJ1

4 0
2 years ago
I just cant remember how to do these ones. been so long<br><br>Solve 2x – 5 = 7​
TEA [102]

Answer:

2x=7+5

2x=12

X=12/2=6

Kskwkjxu

8 0
3 years ago
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