An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle? Express your answer as a mixed number.

Question

mathmate · Answer

The isosceles triangle is made up of two right triangles of measures 3(half base) ,4(height) and 5 (the equal side).
A circle circumscribes the triangle (same as triangle is inscribed in the circle), and has the centre of the circle at the intersection of the perpendicular bisectors.
The perpendicular bisector one of the equal sides cuts the side in two (2.5), and forms a similar triangle with the height.
The radius is therefore the hypotenuse of the smaller triangle, length equal to 2.5*(5/4)=25/8.

An easier way to find the radius of a circumscribed circle is using the formula:
R = b/(2sinB) 
Taking B=one of the equal angles,
sinB=4/5
b=5
so 
R=5/(2*(4/5))=25/8 as before.

anonymous · Answer

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anonymous · Answer

Can you mark the triangle so it becomes clearer how the math works?

mathmate · Answer

I have already drawn up the picture, but the computer with the scanner is not yet available, so I will have it uploaded in abut 10 minutes.  I know the description is confusing!  lol

anonymous · Answer

You can edit my circle above.

mathmate · Answer

I'd rather upload the one that is consistent with my description, sorry.

anonymous · Answer

OK.

anonymous · Answer

Sine rule makes sense. I need to refresh my memory on geometry a bit to be convinced that the lines from a vertex of such a triangle passing through the center are angle bisectors and also perpendicular bisectors.

paxpolaris · Answer

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