This is a problem in hyperbolic geometry c Consider triangle

c. Consider triangle ADCP. Which segments are the three perpendicular bisectors of the sides? Prove that these bisectors are all three parallel to each other.

Solution

PERPENDICULAR BISECTORS IN HYPERBOLIC GEOMETRY: Hyperbolic perpendicular bisector is the geometric place of the points of the plane that are equididtant of two given points

c: given triangle DCP has three perpendicular bisectors

we have to proove that all the perpendicular bisectors are parallel

the theorem on genuine hyperbolic case says that:

the three bisectors in a Triangle are divergingly parallel to each other.there exists a line line perpendicular to all three bisectors. all the three vertices have same distance from L.Hence threre exists a equidistance line through three vertices of the triangle.

hence by this theorem we can say that in the above hyperbolic triangle all the perpendicular bisectors are all parallel to each other.