Circumscribing a Triangle

greatwhiteshark

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May 8, 2005
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NOTE: A = alpha, B = beta Y = gamma

Show that sinA/a = SinB/b = SinY/c = 1/2r where r = the radius of the circle circumscribing triangle ABC whose sides are a, b and c.

HINT: Draw the diameter AB'. Then B = angle ABC = angle AB'C and angle ACB' = 90 degrees.
 
From the hint (though not from the problem) ABC is a right triangle. Draw it with a circle of radis c/2 (so c = 2r) around it and from the definition of sine = opposite/hypotenuse
sin(A) = a/c = a/2r
sin(B) = b/c = b/2r
Sin(C) = 1 = c/c = c/2r
 
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