Tuesday, March 1, 2011

10.5 Angles Related to a Circle!

Hi! Today in class we learned about angles related to circles.
Here are the theorems!


  The first theorem has to do with inscribed angles.The measure of an inscribed angle (vertex of a circle) is one-half the measure of its intercepted arc.                                                  1/2a=x 




Next we have a chord-chord angle        The meaure of a chord-chord angle is one-half the sum of the measures of the arcs intercepted by the chord-chord angle and its vertical angle    
x=1/2(a+b)
 The next angle is a tangent-chord angle.     The measure of a tangent-chord angle is one-half the measure of its intercepted arc.
1/2a=x
 This is a secant-secant angle.  The measure of a secant-secant angle is one-half the difference of the measures of the intercepted arcs.
x=1/2(a-b)


Now we have a secant-tangent angle. The measure of a secant-tangent angle is one-half the difference of the measures of the intercepted arcs.
x=1/2(a-b)




Finally, we have a tangent-tangent angle.  The measure of a tangent-tangent angle is one-half the difference of the measures of the intercepted arcs.
x=1/2(a-b)

                                   
So, in conclusion:
chord-chord angles.........x=1/2(a+b)
inscribed angles or tangent-chord angles..........x=1/2a
tangent-tangent angles, tangent-secant angles, or secant-secant angles............x=1/2(a-b)

Here are some helpful websites:



And you can watch a video where a guy solves a problem with them by clicking

Bye, Hope I helped :D
~Katie

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