Question 850124: Hello, I have been trying to solve this exercise for quite a long time now, and I can't manage to figure it out, so, a little help would be much appreciated.
The question includes a figure, so I took a picture of it and uploaded it, here is a link for it: http://prntscr.com/2yytuo (you may need to copy and paste it into your browser).
Thanks in advance.
(P.S. This question is very important for my exam and I need to understand it because it's my homework and its due tomorrow.)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! you have an isosceles triangle
By dropping a perpendicular from the top of the isosceles triangle to the base and using the Pythagorean Theorem we can determine the height of the triangle
4^2 + x^2 = 12^2
16 + x^2 = 144
x^2 = 128
x = 11.31
now we can calculate the area of the triangle
A = 1/2 * base * height = 1/2 * 8 * 11.31 = 45.24
However, we can split the isosceles triangle into three separate triangles. Because the radius always meets a tangent at a right angle the area of each triangle will be the length of the side multiplied by the radius of the circle. So the total area of the isosceles triangle is given by
(8r/2)+(2×12r/2)= 16r, now the area of the triangle is 45.24, therefore
16r = 45.24
r = 45.24 / 16 = 2.8
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