# Math: PreCal: Triangles

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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 -

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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