For the DS question:
Each statement alone is clearly insufficient.
Taking the combined statement:
Case 1: p=10 and n= 6--->(10+6)(10-6) 16:5 R=1 and 4:3 R=1 and (16*4):15 R=4
Case 2: p=5 and n=1--->(5+1)(5-1) 6:5 R=1 and 4:3 R=1 and (6*4):15 R=9

Since we can get different answers we should choose E.

Now for the geometry problem here is how it goes:
Step 1: calculate the radius of the circle--->R=sqrt((sqrt(3)^2)+1^2)=2
Step 2: Calculate the legth of the hypotenuse of the isosceles right triangle= R*sqrt(2)=2sqrt(2)

Now set up the equations:
Equation 1: s^2+t^2=4 (pythagorean theorem)
Equation 2: sqrt((s+sqrt(3))^2+(t-1)^2)=2sqrt(2) (distance between P and Q = legth of hypotenuse)

Step 3: square Equation 2:
(s+sqrt(3))^2+(t-1)^2=8
s^2+t^2+3+1+2sqrt(3)s-2t=8

Step 4: substitute equation one into equation 2 (s^2+t^2=4)
--->2sqrt(3)s-2t=0

Step 5: Rearrange the terms: t=sqrt(3)*s

Step 6: Plug the possible answer choice and check which one verifies s^2+t^2=4
The only possible answer is 1!
Hope that helped

Thanks!!

I will make sure the answers are hidden next time.

Hi Brent would like to know if my method is correct? THanks