Contesting for Idiot du Jour

[Roger Guay]

Your chance to be Genius du Jour:

If I construct 2 concentric circles, one being half the radius of the larger, then simple math shows that the smaller circle has an area ¼ the area of the larger.
Now if I generate a random point within the radius of the larger circle, I should expect that the probability of it landing in the smaller circle to be ¼.
But, I must be doing something wrong because I get ½ !

Here is my script:

on mouseDown

	getStuff

end mouseDown


local tR, tTheta, tX0, tY0, tX1, tY1, tTotCount, tL, tLongCount

on getStuff

	put item 1 of the loc of grc OuterCircle into tx0

	put item 2 of the loc of grc OuterCircle into tY0

	put "" into tTotCount

	put "" into tLongCount

	emptyFlds

end getStuff


on mouseUp

	lock screen

	repeat 1000

		put random(200) into tR -- 200 is half the width of the larger circle

		if tR > 1 then

			## put random(2*pi) into tTheta1

			get random(360)

			put it*pi/180 into tTheta1

			put tR*cos(tTheta1) into tX1
			put tR*sin(tTheta1) into tY1

			set the loc of grc Ptgrc to tX0 + tX1, tY0 - tY1 --- grc Ptgrc is a 2 pixle oval

			if intersect(grc Ptgrc, grc InnerCircle, "opaque Pixels") then add 1 to tLongCount

			add 1 to tTotCount

		end if

	end repeat
	put tTotCount into fld "totcountFld"

	put tLongCount into fld “LongCountFld"

	put tLongCount/tTotCount into fld "RatioFld"

	unlock screen

end mouseUp


Apparently, this does not generate a random point within the larger circle! Can someone please tell me what’s wrong here?

Thanks,
Roger