Probably Not A Common Sense Question
A square ABCD with an area of 2 exists on the coordinate grid with D at 0,0(and A is 0,sqrt 2).There is a semicircle with diameter CD and a line BE that is tangent to the circle at F.The coordinates of F are in a form of sqrt a + b,sqrt c + d, where a,b,c,d are integers and a and c are not divisible by the square of any prime.What is (a+d)/bc ?
The answer is -0.5.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
By the Two Tangent Theorem BF is sqrt 2 so by the Pythagorean Theorem we have 2=(b^2)+( d^2)(because the problem is translated by sqrt 2,sqrt 2 we know that these will actually be b and d and a and c are both sqrt 2).It is fairly obvious that the only integer solution to this equation is 1,1.However,since f is inside ABCD we must multiply b and d by negative 1.2-1/2*-1=-1/2=-0.5.