Math Is Fun Forum

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

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Circles #4

AB is the diameter of a circle with center O.
C is a point on the circumference such that angle COB = θ
The area of the minor segment cut off by AC is equal to twice the area of the sector BOC.

Prove that

θ is in degrees

Last edited by Agnishom (2014-02-02 00:50:06)

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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Bob

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Registered: 2010-06-20

Posts: 10,140

Re: Circles #4

hi Agnishom,

I must have time to spare today; I'm looking through the unanswered posts; and I found this one.  Did you ever do it?

Use the following:

area of a segment = area of the sector less the triangular bit.

And then you simplify this and use sin(A) = 2 sin(a/2).cos(a/2)

Takes a few lines only. 

Bob

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Children are not defined by school ...........The Fonz
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ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Circles #4

http://www.meritnation.com/ask-answer/question/q-ab-is-the-diameter-of-a-circle-center-o-c-is-a-point-on/areas-related-to-circles/1587959