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The angle will be obtuse if the point lies inside the smaller circle. So the ratio of the areas should be the answer. Sounds right?
points A and B are fixed and they are 2 units apart |dw:1401618811902:dw| the center of our circle is the midpoint of segment AB
is the answer|dw:1401618840569:dw|
the answer is ratio of the area of the shaded region to total area.
we don't know the actual numerical radius of this circle , so we use R it could be R < 1 , in which case A , B would be outside the circle it could be R > 1 , in which case A , B are inside the circle or with R = 1 , A and Bb are on the circle
not exactly sure yet Let's try the case with R = 1 , so that A and B are on the circle . |dw:1401619069277:dw| C must be a point "in" the circle, so I interpret that to be in the interior of the circle.
@bswan this is obtuse |dw:1401619197813:dw|
There certainly "appears" to be an obtuse angle at C .
@bswan |dw:1401619255446:dw| and this is obtuse. And hence the answer I previously proposed.
It should be noted that the question is asking for an obtuse angle in the triangle. So the angles at A and B could be obtuse too. Which is possible only if C lies in the following shaded region: |dw:1401619378172:dw|
|dw:1401619217208:dw| so I would say the probability is the area of double shaded area vs total area of bigger circle
@myko we also need to include the area of the smaller circle.
it is included
bigger circle includes the small one
I meant that the double shaded area must cover the smaller circle too.
so, it looks like it need to be qualified with the condition that R > 1 .
@myko and @Miracrown |dw:1401619632107:dw| is angle C not obtuse here?
nowyou need to calculate what is the angle in black and later integrate from negative to positive of this angle to find the area|dw:1401619688850:dw|
△ABC means the angle at vertex B @nipunmalhotra93
C "is" obtuse for that diagram, yes
@myko dude... that means Triangle ABC.
oh, never mind. You right
read it bad
np... that happens... :)
If you choose C to be in the black-shaded region , is where it appears that we will "not" get an obtuse angle for C . |dw:1401619882929:dw|
so then R must include the condition\(AC^2+CB^2>4\) from one side and what I said befor from the other.
I think you can just say that R > 1. If R <= 1 , the prob (obtuse angle) = 1 .
Very interesting problem, that was.