# How to find a segment's length

• Jul 27th 2010, 06:12 AM
Alhazred
How to find a segment's length
http://img72.imageshack.us/img72/9281/snap1f.jpg
Given the greatest angle and the circle radius I need to calculate the length of A segment.
The circle is tangent to both lines.
How can I do?
• Jul 27th 2010, 06:50 AM
Unknown008
Let's call the centre of the smaller circle O, the point where the small circle touches the semi circle on the horizontal A, the other point which touches the semicircle B and the centre of the semicircle X.

Angle AXB = 116 degrees.
Angle OAX = angle OBX = 90 degrees.

Find angle BOA.
Once found, use the formula for the length of arc AB, that is $s = r\theta$

A segment is an area. (Circular segment - Wikipedia, the free encyclopedia)
• Jul 27th 2010, 07:12 AM
Alhazred
Probably all those lines could confuse.
I have 2 lines, S1 and S2, with a given angle beetween them (in this case is 116 degrees), then I have a circle tangent to both the lines with a given radius (in this case 20).
I need to find a way to calculate the length of the segment AB.

http://img191.imageshack.us/img191/6669/snap1do.jpg
• Jul 27th 2010, 07:18 AM
Unknown008
Oh, that's what you mean. Ok, no problem.

You now can find the angle AOB from your current diagram as I told you earlier. Well, let's call the point where the circle touches the other tangent X.

You know that angle XAB = 116 degrees.
That means angle XOB = 180 - 116 = 64 degrees.
(or [360 - 90 - 90 - 116] since both tangents are 90 degrees)

From there, the angle AOB becomes 64/2 = 32.

From there, you use the trigonometrical ratio tan.

tan 32 = Opp/Adj = AB/20

Solve for AB. (Happy)
• Jul 27th 2010, 09:20 AM
Alhazred
Thenks :)