finding the partial length of a chord (which appears to be the diameter)

I have a circle, diameter and radius unknown. It has a chord running through the center (point "O") and the end points are on the circle. Lets call this chord "SR" This chord SR bisects another chord "TU" and TU has midpoint "K". The only other information I have is that arc angle "TR" formed by point "T" from chord TU and point "R" from chord SR equals 150 degrees; I also have segment "OK" (midpoint "K" of chord TU, and center of circle "O") equals 8*sqrt3. Thats all. I need to figure out what "SR equals

Geometry/Probability

If n points are equally spaced on the circumference of a circle, what is the probability that three points chosen at random will form a right triangle? I know that for us to have a right triangle, the two points should form the diameter of the circle. What I have done is that I divided the problem into two sections. Section I: n even Section II: n odd When n is even it is easier to find the probability but I can't find the right answer (both for n= even and n= odd)

determine a curve

Find the curve that passes through the points (3, 2) and has the property that if the tangent line is drawn at any point P on the curve, then the part of the tangent line that lies in the first quadrant is bisected at P.

Line Intersections

Please show all workings for all parts of the attached line intersection questions. Thanks very much!

A Combination of Algebra and Geometry

Consider the following grid: 1) How many squares (of all sizes) are there in this grid? 2) How many rectangles (of all sizes) are there in this grid? 3) Can you generalize your results to an n by n grid? Can you generalize further? Please see attachment for grid.