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Perpendiculars from the orthocentre to angle bisectors

Source: South African MO 2008 Q5

May 27, 2012

geometrycircumcirclerectanglegeometry unsolved

Problem Statement

Triangle

ABC

has orthocentre

H

. The feet of the perpendiculars from

H

to the internal and external bisectors of

\hat{A}

are

P

and

Q

respectively. Prove that

P

is on the line that passes through

Q

and the midpoint of

BC

. (Note: The ortohcentre of a triangle is the point where the three altitudes intersect.)