Circles: Chords, Radii, and Arcs

Bob · 2012-11-04 06:45:21

You've made up 60 and 30 because that's what those angles look like. But remember D could be anywhere on the circumference.

I've added a few more possibilities in different colours.

But in a way you're right because the angle at D is always ...... ?

Bob

zee-f · 2012-11-04 06:48:13

when I measure the one you drew on the screen I get A is 30 degrees C is 70 D is 80

zee-f · 2012-11-04 06:49:29

I said #102 before seeing post #101

zee-f · 2012-11-04 06:54:59

is always a right angle right?

Bob · 2012-11-04 06:56:35

The thing is this. There is a property that is always true for all circles and Q19 is testing it.

Amongst all your answers, you have said it correctly, but I don't want you to get it by luck, I want you to be sure.

So, looking at my multi-coloured diagram, what is angle D every time?

Bob

Bob · 2012-11-04 06:57:46

Yes, that's it. Excellent!

Bob

zee-f · 2012-11-04 07:21:38

Thank you for the help!

Bob · 2012-11-04 07:23:13

You are very welcome.

By my reckoning only Q20 to go or have you done that?

Bob

zee-f · 2012-11-04 08:48:51

No I did #20 and got it correct

I choose D

20. If line segment BC has a length of 24, and line segment AB has a length of 18, what is the radius of the circle?
A 18
B 38
C 6
D 15
E 4
F 29

zee-f · 2012-11-04 09:16:59

I started the next lesson about Circumference and Arc Length and I got all the 18/20
I am stuck on the 2 questions I got incorrect :

I choose C it was incorrect

What is the circumference of the circle if the radius is:

10. (x + y)pi

A (x+y)/7
B (x+y)/5
C(x+y)/1
D(x+y)/2
E (x+y)/3
F (x+y)/8

So I know the the formula for the circumference of a circle is 2(pi)(r)

So it would be 2(pi)*((x + y)pi) right? but then what do I do ?

I choose A it was incorrect I am still working on the correction
What is the length of the arc if
15. r=y n=x
A x*y*pi/90
B x*y*pi/30
C x*y*pi/45
D x*y*pi/27
E x*y*pi/180
F x*y*pi/115

L =
(n/360)(2(PI)r) where L = length, n = degree measure of arc, and r = radius of the circle.

Last edited by zee-f (2012-11-04 09:18:58)

Bob · 2012-11-04 10:47:37

hi zee-f

Very well done for getting 18/20 at first attempt. That's really good!

I can see where you went wrong here with Q15, so I'll do it first.

I choose A it was incorrect I am still working on the correction
What is the length of the arc if
15. r=y n=x
A x*y*pi/90
B x*y*pi/30
C x*y*pi/45
D x*y*pi/27
E x*y*pi/180
F x*y*pi/115

With these problems I first work out the whole circumference, and then work out the fraction for the arc.

So cancel a 2 top and bottom and it's done.

Now for question 10.

What is the circumference of the circle if the radius is:
10. (x + y)pi
A (x+y)/7
B (x+y)/5
C(x+y)/1
D(x+y)/2
E (x+y)/3
F (x+y)/8
So I know the the formula for the circumference of a circle is 2(pi)(r)
So it would be 2(pi)*((x + y)pi) right? but then what do I do ?

What you have done is exactly right so something else is wrong here.

If the radius has a pi in it, the circumference will collect another, giving a pi squared. None of the answers looks right.

If it's a mis-print I can make sense of it. Try this:

What is the radius of the circle if the circumference is:

10. (x + y)pi

A (x+y)/7
B (x+y)/5
C(x+y)/1
D(x+y)/2
E (x+y)/3
F (x+y)/8

This way round it makes sense and one of the answers works.

Bob

zee-f · 2012-11-06 08:09:01

Hi Bob,

15. r=y n=x

#15- My new answer is (E) x*y*pi/180

I pretended that x was 1 and said that
(1/360 * 2= 1/180) then put the x back and multiplied. I get x*y*pi/180.

#10- OK sense I know that c=π*d and D= c/π
I am going to divide the circumference by PI So I will get(x+y)π/π , and
π/π = 1 so I am left with (x+y) and to get the radius I am going to divide by two and my answer is (x+y)/2.

Thank you,

Bob · 2012-11-06 09:54:21

hi zee-f

Oh, well done. I'm so pleased. Both correct in my opinion.

Bob

Math Is Fun Forum

#101 2012-11-04 06:45:21

Re: Circles: Chords, Radii, and Arcs

#102 2012-11-04 06:48:13

Re: Circles: Chords, Radii, and Arcs

#103 2012-11-04 06:49:29

Re: Circles: Chords, Radii, and Arcs

#104 2012-11-04 06:54:59

Re: Circles: Chords, Radii, and Arcs

#105 2012-11-04 06:56:35

Re: Circles: Chords, Radii, and Arcs

#106 2012-11-04 06:57:46

Re: Circles: Chords, Radii, and Arcs

#107 2012-11-04 07:21:38

Re: Circles: Chords, Radii, and Arcs

#108 2012-11-04 07:23:13

Re: Circles: Chords, Radii, and Arcs

#109 2012-11-04 08:48:51

Re: Circles: Chords, Radii, and Arcs

#110 2012-11-04 09:16:59

Re: Circles: Chords, Radii, and Arcs

#111 2012-11-04 10:47:37

Re: Circles: Chords, Radii, and Arcs

#112 2012-11-06 08:09:01

Re: Circles: Chords, Radii, and Arcs

#113 2012-11-06 09:54:21

Re: Circles: Chords, Radii, and Arcs

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