The area of a triangle inscribed in a circle is 60m^2 and the radius of the circumscribed circle is 8cm. If the two sides of the inscribed triangle measure 10 cm and 12 cm, find the length of the third side.

Question

anonymous · Answer

@perl

anonymous · Answer

@Directrix

anonymous · Answer

@jim_thompson5910  help me please :D

jim_thompson5910 · Answer

I don't think it's possible, but I'm still trying various methods out.

anonymous · Answer

I think you can do herons formula here

jim_thompson5910 · Answer

yeah you would solve the following for x

$$\Large \sqrt{s(s-10)(s-8)(s-x)} = 60$$

where $\Large s = \frac{10+8+x}{2}$

jim_thompson5910 · Answer

the thing is though, I'm getting nonreal answers for x

jim_thompson5910 · Answer

These are the approximate solutions the computer gives me

-14.25982084+6.272359244i
14.25982084-6.272359244i
-14.25982084-6.272359244i
14.25982084+6.272359244i

none of which are a real number

jim_thompson5910 · Answer

oh my bad, I typed it in wrong

jim_thompson5910 · Answer

one second while I fix it

jim_thompson5910 · Answer

ok, fixed

solve the following for x

$$\Large \sqrt{s(s-10)(s-12)(s-x)} = 60$$


where $\Large s = \frac{10+12+x}{2}$

jim_thompson5910 · Answer

The only issue I have with this now is that the triangle isn't 100% on the circle. I'm using geogebra and I can't get all 3 points to lie on the circle.

anonymous · Answer

@Directrix

directrix · Answer

I worked on this problem last night. This thread shows what those before me had done. http://openstudy.com/users/directrix#/updates/54ecca39e4b06b22807cc9f1

anonymous · Answer

ok thnx

anonymous · Answer

can you help me with another problem

directrix · Answer

I am not sure that the current problem has been solved. The triangle that had to be right was off a bit.