actually reflection of orthocentre about a line lies on the circumcircle of the trianlge hence from the diagram HP = PD
we need to find HD
so by knowing the value of HP it's done,
we know by property of triangle that
height of orthocentre frm a side is given by ( as here HP ) = 2Rcos Bcos C
so required value of HD = 2 x HP = 4Rcos B cos C.
Note : if height was to be measured frm AC then value = 2Rcos A cos C
and if frm AB the value wuld have been 2R cos A cos B