Circles: Chords, Radii, and Arcs

Bob · 2012-10-30 05:07:44

OK. Post if you need to. I'll try to be more awake!!

Bob

zee-f · 2012-10-30 08:29:16

Hey again,

I answered #11 wondering if it's correct

#11- I choose C
11. What is the measure of arc AC?
A 54 deg
B 137 deg
C 180 deg
D 111 deg
E 174 deg
F 23 deg

Bob · 2012-10-30 08:33:23

That makes sense. It must be a diameter.

Bob

zee-f · 2012-10-31 01:12:16

#12- I choose 4(D) because the hypotenuse is two times that of the leg opposite the 30 degree angle. The leg opposite the 30 degree angle is 60 degree angle and the question said AB is 4 So, I multiply 4 * 2=8 and the radius = 1/2 * 8 = 4 So that is my answer.

12. If ABC is a 30-60-90 triangle, with angle ACB at 30 degrees, and line segment AC is the diameter of the circle, then if the length of line segment AB is 4, what is the radius of the circle?

A 8
B 2
C 10
D 4
E 7
F 16

#13- I choose A

13. Working with the information from 12 from here to #16, what is the measure of arc AB?
A 90 deg
B 25 deg
C 30 deg
D 120 deg
E 60 deg
F 72 deg

#14- F

14. What is the measure of arc BC?
A 20 deg
B 45 deg
C 75 deg
D 120 deg
E 15 deg
F 90 deg

15- E

15. Are arcs ABC and AC equal?
A maybe
Bnone of these
Ckinda
D55
E yes
F no

I was wondering how I can find that ?

16. What is the measure of chord BC?
A 6.928
B 2.098
C 5.281
D 10.112
E 9.475
F 7.461

Last edited by zee-f (2012-10-31 02:56:10)

bobbym · 2012-10-31 03:00:39

Hi;

I like 12 D too.

Bob · 2012-10-31 03:58:59

hi zee-f

12D is good for me too.

13F Don't think so. Just to check ... for an arc the measure is the angle it makes at the centre of the circle ??

14F Also here I get a different answer.

15E Yes

16 If Ois the centre of the circle, what are the angles in triangle OBC ?

Bob

zee-f · 2012-10-31 04:22:51

13- The measure of an inscribed angle is equal to one-half the degree measure of its intercepted arc.

Bob · 2012-10-31 05:17:31

hi zee-f

The measure of an inscribed angle is equal to one-half the degree measure of its intercepted arc.

That cannot be right. Look at these earlier answers:

#2- I choose B
2. If the measure of arc BFE is 80 degrees, then what is the measure of angle BME?
A 37 deg
B 80 deg
C 9 deg
D 23 deg
E 17 deg
F 41 deg
3. If there were an imaginary angle ACB, what would the measure of that angle be? (Hint: Remember that a line is an angle with a measure of 180 degrees, or that a circle has a total arc measure of 360 degrees.)
#4- I choose E
4. If angle EMA has a measure of 100 degrees, what is the measure of arc EDA?
A 77 deg
B 180 deg
C 15 deg
D 26 deg
E 100 deg
F 164 deg

In all these cases the 'measure of an arc' is the angle the arc makes at the centre of the circle.

I think you may be getting confused with something else.

Bob

zee-f · 2012-10-31 06:03:23

But weren't these talking about a central angle The measure of a central angle is equal to the length of the arc it defines. and we are talking about an inscribed angle now right ?

Bob · 2012-10-31 06:08:31

What do you mean by an inscribed angle?

Question 13 doesn't say anything about an inscribed angle.

#13- I choose A
13. Working with the information from 12 from here to #16, what is the measure of arc AB?
A 90 deg
B 25 deg
C 30 deg
D 120 deg
E 60 deg
F 72 deg

Let's take a step back from what the words mean and look at the diagram. I've reproduced it again below.

What are the following angles:

ACB = 30
ABC =
BAC =
AOB =
ABO =
OBC =
BOC =

Bob

zee-f · 2012-11-01 05:12:21

Acb = 30
Abc = 90
Bac = 60
Aob = 30
Abo = 90
Obc = 90
Boc = 60

Last edited by zee-f (2012-11-01 05:30:14)

zee-f · 2012-11-01 05:31:27

So my answer would be the arc of AB= 30

zee-f · 2012-11-01 05:36:47

14- E

14. What is the measure of arc BC?
A 20 deg
B45 deg
C75 deg
D120 deg
E 15 deg
F 90 deg

Bob · 2012-11-01 05:57:07

hi zee-f

Do you have a compass and protractor? You might find it helpful to make your own accurate drawing.

(i) Draw a circle.
(ii) Put on one diameter AC.
(iii) Measure a 30 degree angle at C and find the point B on the circle.
(iv) Check that ABC = 90.

Acb = 30

Correct!

Abc = 90

Correct, well done!

Bac = 60

Correct, well done!

Aob = 30

How did you get this? Look at triangle AOB. What sort of triangle is it?

Abo = 90

This is also not correct. When you get AOB right, I think you'll find you can get this one right too.

Obc = 90

The diagram is accurately drawn. Does this angle look like 90 ? Look at triangle BOC. What sort of triangle is it?

Boc = 60

This answer will follow on from the answer to OBC

Now what about Q14 ?

I don't think this is answer E.

You should be giving the size of angle BOC here, so when you've got that right Q14 will be easy.

Bob

zee-f · 2012-11-01 08:02:58

It's an Acute Triangle so all the angles are less then 90.

Abo = 45
Obc = 45
Boc = 15

And when I add 45+15+30+45+15+30= 180 So that makes it correct.

Last edited by zee-f (2012-11-01 08:14:29)

zee-f · 2012-11-01 08:20:41

14.I choose E- 15°

14. What is the measure of arc BC?
A 20 deg
B 45 deg
C 75 deg
D 120 deg
E 15 deg
F 90 deg

15- I choose E-Yes

15. Are arcs ABC and AC equal?
A maybe
B none of these
C kinda
D 55
E yes
F no

Bob · 2012-11-01 09:01:39

hi zee-f

15 E yes. Correct!!

But you still haven't got 13 and 14 sorted out.

Did you try actually making a drawing.

Remember that A to O to C is a diameter and so also a straight line.

That means the angle CAB is the same as OAB. And you already know the measure of CAB.

And the triangle ABO has got three acute angles, true, but it's a bit more special than that.

Two of its sides are equal to the radius.

But don't say isosceles either.

Can you see that one of its angles is 60 degrees.

That makes it even more special.

Do you own a protractor? That's a plastic measuring device for angles. You can get semi-circular ones and also full circle ones.

Picture below.

Bob

zee-f · 2012-11-01 09:10:53

Yes I own a protractor So that makes Ab= 60 bc= 75

Bob · 2012-11-01 09:23:25

We make progress. Arc AB is 60.

But BC is not 75.

See picture.

Bob

zee-f · 2012-11-01 09:41:43

120

Bob · 2012-11-01 09:43:28

Excellent!

So now let's recap all those answers.

ACB = 30
ABC =
BAC =
AOB =
ABO =
OBC =
BOC =

Bob

zee-f · 2012-11-01 09:54:52

Acb = 30
Abc = 90
Bac = 60
Aob = 30
Abo = 60
Obc = 120
Boc =60

Bob · 2012-11-01 10:03:26

Still not all correct.

Give me a moment to make a new picture.

Bob

Bob · 2012-11-01 10:15:34

Acb = 30 tick
Abc = 90 tick
Bac = 60 tick
Aob = 30 X
Abo = 60 tick
Obc = 120 X
Boc =60 X

These last two look like you are measuring the wrong angles.

Bob

In my rush to make the pictures I've chopped off the text It should read "this is angle OBC, centre of protractor at B, measure angle between lines OB and BC"

zee-f · 2012-11-01 10:28:52

Aob = 60
Obc = 30
Boc = 120

Math Is Fun Forum

#51 2012-10-30 05:07:44

Re: Circles: Chords, Radii, and Arcs

#52 2012-10-30 08:29:16

Re: Circles: Chords, Radii, and Arcs

#53 2012-10-30 08:33:23

Re: Circles: Chords, Radii, and Arcs

#54 2012-10-31 01:12:16

Re: Circles: Chords, Radii, and Arcs

#55 2012-10-31 03:00:39

Re: Circles: Chords, Radii, and Arcs

#56 2012-10-31 03:58:59

Re: Circles: Chords, Radii, and Arcs

#57 2012-10-31 04:22:51

Re: Circles: Chords, Radii, and Arcs

#58 2012-10-31 05:17:31

Re: Circles: Chords, Radii, and Arcs

#59 2012-10-31 06:03:23

Re: Circles: Chords, Radii, and Arcs

#60 2012-10-31 06:08:31

Re: Circles: Chords, Radii, and Arcs

#61 2012-11-01 05:12:21

Re: Circles: Chords, Radii, and Arcs

#62 2012-11-01 05:31:27

Re: Circles: Chords, Radii, and Arcs

#63 2012-11-01 05:36:47

Re: Circles: Chords, Radii, and Arcs

#64 2012-11-01 05:57:07

Re: Circles: Chords, Radii, and Arcs

#65 2012-11-01 08:02:58

Re: Circles: Chords, Radii, and Arcs

#66 2012-11-01 08:20:41

Re: Circles: Chords, Radii, and Arcs

#67 2012-11-01 09:01:39

Re: Circles: Chords, Radii, and Arcs

#68 2012-11-01 09:10:53

Re: Circles: Chords, Radii, and Arcs

#69 2012-11-01 09:23:25

Re: Circles: Chords, Radii, and Arcs

#70 2012-11-01 09:41:43

Re: Circles: Chords, Radii, and Arcs

#71 2012-11-01 09:43:28

Re: Circles: Chords, Radii, and Arcs

#72 2012-11-01 09:54:52

Re: Circles: Chords, Radii, and Arcs

#73 2012-11-01 10:03:26

Re: Circles: Chords, Radii, and Arcs

#74 2012-11-01 10:15:34

Re: Circles: Chords, Radii, and Arcs

#75 2012-11-01 10:28:52

Re: Circles: Chords, Radii, and Arcs

Board footer