<p>“Points X and Y are two different points on a circle. Point M is located so that line segments XM and YM have equal length. Which could be true?”</p>
<p>I. M is the center
II. M is on arc XY
III. M is outside</p>
<p>If you say that two points are on a circle, does that mean that those two points are on the circumference, or anywhere inside the circle?</p>
<p>Yes, ‘on’ the circle means ‘on the circumference’.
If it is inside the circle, the question will mention ‘inside’.
( grammatically, in the circle also means inside the circle, but that might not be asked on the SAT, since that seems confusing.)
actually, the answer should be all three i.e. I, II and III.
I and II are obviously true…
For III, suppose X and Y are the ends of a diameter . If a tangent is drawn to X AND Y , both the tangent pass through a point, say M.
so XM=YM
proved!!</p>