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### Geometry Proof - The Inscribed Angle is 1/2 of the Central Angle

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Date: 2/12/96 at 12:25:59
From: Anonymous
Subject: Geometry Question

I am in grade 7 but I have passed the grade 7 and 8 courses and am
just doing all the unit tests in the grade 9 book before taking that
exam.

The grade 9 math book describes the relationship between a central
angle and an inscribed angle (the inscribed angle is 1/2 the central
angle).  I would like to see that proven.  Where can I find a proof or
do you know how to prove it or can you offer a hint as to what path to
take to prove it?

Thanks,
Daniel
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Date: 2/14/96 at 18:36:47
From: Doctor Byron
Subject: Re: Geometry Question

Hi Daniel,

Here's an idea for you to go on:  Draw a circle with center C.  Now
add an arc AB to the circle.  Draw the radii AC and BC which connect the
endpoints of the arc to the center.  Now add the vertex of the inscribed
angle, I, and draw AI and BI.  Finally, add the diameter through C and I.

You will notice that you now have two congruent isoceles triangles to
work with (since CB, AB, and CI are all radii, they are congruent).
Using the nature of these triangles, and remembering the fact that the
angles in all triangles sum to 180 degrees, you should be able to find

Good luck, and keep up the good work in math!

-Doctor Byron,  The Math Forum

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Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry

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