# Geometry Circle Problem

• Apr 2nd 2012, 06:08 PM
Proclivitas
Geometry Circle Problem
• Apr 2nd 2012, 06:28 PM
Wilmer
Re: Geometry Circle Problem
Check your post...are you sure about the 120? Doesn't that look impossible to you?!
Looks more as if the angle is 120 degrees, and you're to find arc's length...
• Apr 2nd 2012, 06:36 PM
Proclivitas
Re: Geometry Circle Problem
Quote:

Originally Posted by Wilmer
Check your post...are you sure about the 120? Doesn't that look impossible to you?!
Looks more as if the angle is 120 degrees, and you're to find arc's length...

The measure of the arc is 120* as it says in the picture >.> and the measure of the arc is the same as the central angle, 120*.
• Apr 2nd 2012, 07:56 PM
Wilmer
Re: Geometry Circle Problem
I can't make out what you're saying...an arc has a LENGTH...perhaps someone else will...
• Apr 2nd 2012, 10:50 PM
earboth
Re: Geometry Circle Problem
Quote:

Originally Posted by Proclivitas

1. Have a look here: Inscribed angle - Wikipedia, the free encyclopedia

2. As far as I understand your question you have to evaluate the length of the radius first. Use the indicated right triangle. Keep in mind that $\displaystyle \sin(60^\circ) = \frac12 \sqrt{3}$

3. To determine the length of C use proportions:

$\displaystyle \frac C{2 \pi r} = \frac{120^\circ}{360^\circ} = \frac13$
• Apr 3rd 2012, 12:16 AM
biffboy
Re: Geometry Circle Problem
Divide triangle into two right angled triangles
Let r=radius. So sin60=3/r root3/2=3/r r=6/root3=6root3/3=2root3
area sector 1/3pir^2 =1/3pi.12=4p

Let height of triangle =h Then tan60=3/h h=3/tan60=root3
Area of triangle=1/2.6.root3=3root3
Segment=sector-triangl
• Apr 3rd 2012, 06:23 AM
Wilmer
Re: Geometry Circle Problem
That's not what's asked for, Biff.

The problem, PROPERLY worded:
chord AB = 6 cm
angle AOB = 120 degrees
calculate length of arc ACB

...to which Earboth shows the steps to solution.
An arc SUPPORTS a central angle; is NOT equal to a number of degrees:
it has its own length, which is part of the circle's circumference.
• Apr 4th 2012, 04:45 PM
bjhopper
Re: Geometry Circle Problem
The problem asks for the angle AOB, sector area OACB,and segment areaACB.Biff in his last post defines sector area = 4pi and the sector triangle area 3rad3.Both correct.He didn't finish to find the segment area.
• Apr 4th 2012, 10:03 PM
biffboy
Re: Geometry Circle Problem
Area segment=area sector-area triangle=4pi-3root3