SOLUTIONWhat is the radius of the circle above with center O?
(1) The ratio of OP to PQ is 1 to 2.
(2) P is the midpoint of chord AB.
The answer to this question is straight E. Even when we consider the statements together we only have the ratios, not absolute values of any line segment.
Would anything have changed if they either A) Provided the area of QPB or B) If they mentioned that the AB was the radius and it was cut in half?
My guess is that if they provided the area, we could get the value of AQB and equate the earlier ratio of OP to PQ. This would give us the diameter essentially and we could get the radius from that. Is that correct?