Given a circle of radius r, we choose randomly four points (a, b, c, and d) inside the circle. Then we draw the segment ab, connecting the points a and b, and the segment cd, connecting the points c and d.So what's the probability that the segments intersect each other ?
Please explain the solution.
2006-09-11 07:53:55 · 5 answers · asked by FauxPas 2 in Science & Mathematics ➔ Mathematics
This question was asked and answered recently.
2006-09-11 08:00:36 · answer #1 · answered by helene_thygesen 4 · 0⤊ 0⤋
To clarify... the other question IS NOT THE SAME AS THIS ONE.
That one clearly stated the points were on the edge... in which case it is a simple subset of this problem.
However one should point out that how you define random matters.
If by random you mean with uniform distribution over the circle then im sure the answer is easy with some thought... respond to that and i will attempt it.
2006-09-11 15:07:24 · answer #2 · answered by Anonymous · 0⤊ 0⤋
as the points are inside the circle and not on the circumference , the number of such orientations is infinite for which the lines shall intersect and also total number of possibilites is infinite. so the net probabitity is infinite/infinite , which is underminate form.
but if u consider a fixed number of orientations , the answer will be tending to 1
2006-09-11 08:06:14 · answer #3 · answered by Anonymous · 0⤊ 0⤋
*if the lines ab & cd are parallel, they will never intercect;
*if the lines ab & cd are perpendicular, the intersection of the lines are infinite due to ploting, angles, and the circle size
...i think?
2006-09-11 07:58:35 · answer #4 · answered by curious moper 6 · 0⤊ 1⤋
they will intersect inside or outside if they are not parallel
so the probability is almost 1 that they will intersect either inside the circle or outside
2006-09-11 07:56:57 · answer #5 · answered by raj 7 · 0⤊ 1⤋