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Inscribed Angle, Circle Equation


Date: 6/14/96 at 14:58:44
From: Anonymous
Subject: Inscribed angle, circle equation

What's an inscribed angle? What's the equation for the center of the 
circle of (8,-1) with radius 15?


Date: 6/19/96 at 14:53:47
From: Doctor Paul
Subject: Re: Inscribed angle, circle equation

Let's first talk about inscribed angles..

Here's the dictionary definition: to draw within a figure so as to 
touch in as many places as possible (a regular polygon inscribed in a 
circle).

So... to inscribe an angle in a circle, put the vertex at one point on 
the circle and make sure that the rays leading away from the vertex 
also touch the circle (at places other than the vertex, of course).

I think you misphrased the second question.  Here's what I think you 
meant to ask:

What is the equation of the circle with center (8,-1) and radius 15?
To do this problem you need to know the formula.  Here it is:
(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the 
radius.

In your specific case, h is 8, k is -1, and r is 15
to complete the problem, just plug h, k, and r into the equation 
I gave you above..

(x-8)^2  + (y-(-1)^2 = 15^2
now recall that subtracting a negative number is really adding...
so y-(-1) is really y+1

(x-8)^2 + (y+1)^2 = 225

It would be perfectly okay to expand this out, but equations of 
circles are usually left in this form because it is much easier to 
tell what the coordinates of the center and the radius of the circle 
are.

-Doctor Paul,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Conic Sections/Circles
High School Coordinate Plane Geometry
High School Geometry

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