Posted by **Joey** on Wednesday, March 28, 2012 at 1:23am.

An isosceles triangle is inscribed in a circle. The shortest side is the base which is 16 cm long. If the radius of the circle is 10 cm, what is the length of side "a"?

- Math: PreCal: Triangles -
**Reiny**, Wednesday, March 28, 2012 at 8:19am
I will assume "a" is one of the equal sides of the triangle

make a sketch, by drawing in the altitude to the base of the triangle.

draw in the radius to the base vertex.

You will have a right-angled triangle with sides 8 and x and hypotenuse 10

x^2 + 8^2 = 10^2

x = 6 ( you might have recognized the 3-4-5 right-angled triangle multiplied by a factor of 2 )

So the altitude is 6+10 = 16

Now you have a large right-angled triangle with sides 8 and 16 with hypotenuse "a"

a^2 = 16^2+8^2 = 320

a = √320 = 8√5

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