Submitted by 6sigma on Tue, 03/28/2017 - 17:39
Forums:
Another geometry question...
I really have no idea how to start problem #8 (other than drawing a picture). The hint said I would need to use some circle theorems, but I can't think of any that would help.
Thanks!
Label the points where the
Label the points where the circle touches the triangle. If BC is the hypotenuse of the triangle and X is the touching of the circle and hypo, what is the length of CX (in terms of b and r)? The diagram should help make this clear. What about BX (in terms of c and r)? But you know that BC = a = CX + BX. This should give you $a$ in terms of $r,b,c$ which should hopefully get you the right thing.
Maybe try using areas
Hiya!
Try taking into account areas and don't forget Pythagoras for the first bit :)
My method wasn't the best but it worked and gave '2r=b+c (+or-) a', then after a small explanation that if r=(a+b+c)/2 then this would be greater than a on it's own so it must be 2r=b+c-a.
Hope this helps! :)