What conditions would be enough to prove that P is the circumcenter of HJK ? Select all that apply.
There is a triangle HJK in which M, N and L are the points on the side HJ, side JK and side HK respectively. Segment HP is the angle bisectors of angle KHJ, segment JP is the angle bisectors of angle HJK, and segment KP is the angle bisectors of angle JKH. Segment HP, segment JP, and segment KP intersect each other at point P. Segment MP is perpendicular to side HJ, segment NP is perpendicular to side JK, and segment LP is perpendicular to side HK. The length of PM is 6x-14 and the length of LP is 3x+4.
A. L, M, and N are the midpoints of HK¯¯¯¯¯¯, HJ¯¯¯¯¯ and KJ¯¯¯¯¯ .
B. PL¯¯¯¯¯≅PM¯¯¯¯¯¯≅PN¯¯¯¯¯¯
C. PK¯¯¯¯¯¯≅HP¯¯¯¯¯¯≅PJ¯¯¯¯¯
D. △HJK is an acute triangle.
