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#1 2014-02-02 00:49:48

Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 22,387

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)

'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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#2 2014-05-22 01:07:26

bob bundy
Registered: 2010-06-20
Posts: 7,378

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.  smile


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei


#3 2014-05-22 01:56:08

Registered: 2011-02-07
Posts: 3,646

Re: Circles #4


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