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Expert: - 3/28/2009


Question
i m studying in 8th std. and i don't know how to measure the subtended arcs and cyclic quadrilateral.

Answer
Subtended Arc

The subtended arc is how much of a circle.
There are 360 degrees or 2pi radians in a whole circle.
The area of an entire circle is pi*rē.

If a subtended arc is taken that is 1/4 of the circle,
its angle is 90 degrees or pi/2 radians.
The area of that section is pi*rē/4.

If a subtended arc is taken that is 1/6 of the circle,
its angle is 60 degrees or pi/3 radians.
The area of that section is pi*rē/6.


Cyclic Quadrilateral

A cyclic quadrilateral is one in which a circle can be found
whose edge contains all of the corners of that quadrilateral.
This means that there is some point in the center of this
quadrilateral that is at and equal distance from all of the corners.

Let the length of the sides be a, b, c, and d and let s = (a+b+c+d)/2.

Then the area of this cyclic quadrateral has to do with the side lengths and s.  The equation to find the area is
√((a-s)(b-s)(c-s)(d-s)).

I found this in the paper http://jwilson.coe.uga.edu/emt725/brahmagupta/brahmagupta.html ,
which has other interesting stuff in it.

I looked at over two dozen documents, but found no reference to the radius of a cyclic quadrilateral.

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