What is the probability that a randomly drawn chord will be longer than the radius of the circle?
What is the probability that a randomly drawn chord will be the exact same length as the radius of the circle?
That said, I think the answer that DJ is looking for is 2/3 as others have figured.
my way of explaining:
>6 equilateral triangles can fit inside a circle.
(a picture does help)
>Take any two of these triangles that are next to each other.
>The triangles share 2 points: the center of the circle and a point you can defined as the arbitrary starting point of the chord.
>The other two points of the triangles- the most distant points- define 1/3 the circumference of the circle.
>If a chord is drawn from the arbitrary starting point to a point within this area it will be shorter than the radius.
>You can see how this is true because the two sides of the triangles which are chords themselves are the same lenth as the radius.
>Therefore, a chord drawn from the starting point to the other 2/3rds of the circle will be longer than the radius.
Posted by geoffrey
on 2003-10-09 17:16:55