Cant understand this solution in certain points

[nhrock3]

on a circle with radius 1 there are two points one is static the other is
distributed evenly on the circle (i don't know the proper english term)
we sign X to be the hypotenuse on the circle

find the density function of the variable X
?

solution(i partialy understood it)the questions come after the photo

they say that we take x to be an angle from o til pi/2
we scan only the northern hemisphere because its symmetric.

what is the curv graph represents
what is t?
what is the meaning of y<=t?
why if they say that x should go from o til pi/2?
in the probability function they put x fro 0 till arcsin t/2 where t goes from
0<t<=2
?

after this step they did the derivative to find the density function
i understand that step

 

[tiny-tim]

Hi nhrock3!

(have a pi: π and a ≤ )

on a circle with radius 1 there are two points one is static the other is
distributed evenly on the circle (i don't know the proper english term)
we sign X to be the hypotenuse on the circle

find the density function of the variable X
…
they say that we take x to be an angle from o til pi/2
we scan only the northern hemisphere because its symmetric.

what is the curv graph represents
what is t?
what is the meaning of y<=t?
why if they say that x should go from o til pi/2?
in the probability function they put x fro 0 till arcsin t/2 where t goes from
0<t<=2
?

after this step they did the derivative to find the density function
i understand that step

(we usually say "uniformly", but "evenly" is also ok and we usually say "around a circle")

No, I don't think x is the hypotenuse.

It's a little difficult to tell, but I think x and y are angles …

(and what is t … is it a chord? )

Let's call the fixed point A, the movable point X, and the centre O. And let B be the other end of the diameter AOB.

Then I think x is the angle between the two points, which equals AOX, and y is the angle ABX.

y is always x/2 (if you don't know that, you need to look at a geometry book).

Carry on from there. ​

 

[nhrock3]

you are correct its a hord not a hipottenuse
but you didnt answer my questions?