let ABC be an acute angled triangle whose orthocentre at H. altitude from A is produced to meet circumcircle of the triangle ABC at D. then the distance HD is.....??
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2 Answers
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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
