Geometry Proof - The Inscribed Angle is 1/2 of the Central Angle
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
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 your proof. Good luck, and keep up the good work in math! -Doctor Byron, The Math Forum
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