15) In the figure, point P is the circumcenter of Delta JKL Which of the following statements must be true? I. PX=PY II. PJ=PK III. PK=PL A Ionly B II only C III only D II and II only E I,II, and III

Given that point P is the circumcenter of triangle JKL, we can deduce the following properties:- The circumcenter of a triangle is equidistant from all three vertices of the triangle.- The circumcenter is the point from which if you draw circles (circumcircles), they would pass through all three vertices of the triangle.Based on these properties, we can analyze the statements given:I. \(PX = PY\)Since P is the circumcenter, PX and PY are radii of the circumcircle to the points where the perpendiculars from P meet sides JK and JL, respectively. However, without knowing that these sides are equal, we cannot conclude that PX and PY are equal just from P being the circumcenter. This statement is not necessarily true.II. \(PJ = PK\)This statement must be true because P is the circumcenter, and PJ and PK are the distances (radii) from the circumcenter to the vertices J and K, respectively. Since the circumcenter is equidistant from all vertices, \(PJ = PK\).III. \(PK = PL\)This statement must also be true because P is the circumcenter, and PK and PL are the distances (radii) from the circumcenter to the vertices K and L, respectively. Since the circumcenter is equidistant from all vertices, \(PK = PL\).Therefore, the correct statements are II and III, which means the correct answer is:D) II and III only