9. As can be seen from Figure 2, X and Y satisfy the relationship of xy=C, and c is a constant. As can be seen from the point in Figure 2, when x=3 and y=3, then C=9. Triangle AEF is an isosceles right triangle and ABCD is a rectangle, so triangle EBC and triangle CDF are both isosceles right triangles. So, EB=BC, CD=DF. Therefore, when x=3, EB=BC=CD=DF, and only point C and point M can meet the conditions, so at this time, EC=EM and A are wrong; When y=9, as can be seen from Figure 2, X

10, a: when the chord of PB is the longest, that is, PB is the diameter, it can be known that the triangle APC is an isosceles triangle, and the angular relationship is 30 degrees, 30 degrees, 120 degrees; Item B: When the triangle APC is an isosceles triangle, there are two cases, one is that the point P is on the arc AC, the other is that P and B coincide, and both cases are that OP is perpendicular to AC; Item C: When OP is perpendicular to AC, the above two situations are still the same, but when point P coincides with point B, the angle ACP=60 degrees, and C is wrong; Item D: When the angle ACP is equal to 30 degrees, there are two situations, one is that the point P is on the arc AC, and the other is that the point P is on the arc AB. Obviously, in these two cases, either BP crosses point O or CP crosses point O, and the triangle BCP is a right triangle.