+194 Triangle ABC is a 30-60-90 right triangle with right angle at C, angle ABC = 60 degrees, and hypotenuse of length 2. Let P be a point chosen at random inside ABC, and extend ray BP to hit side AC at D. What is the probability that BD < √2?
+130466 
BC = 1
AC = sqrt 3
AB = 2
Construct a circle at B = (1,0) with a radius of sqrt 2
The equation of the circle is (x -1)^2 + y^2 = 2
To find the intersection of BD and AC let x = 0
Then y = 1
So D = (x ,y) = (0, 1)
BD = radius of the circle = sqrt 2
DC =1
The probability that BD < sqrt 2 is DC / AC = 1 / sqrt 3 ≈ 57.7 %
