See diagram. By definition of the Orthocentre to prove that is theOriginally Posted bythduong711

orthocentre of triangle it is sufficient to prove that extended

is a normal to , and that extended is a normal to .

Now it is sufficient to prove that in general extended is a normal ,

as by an equivalent argument will be a normal to .

Now the best way to proceed as far as I can see is to introduce

coordinates, and use coordinate geometry to show that angle

in the diagram is a right angle.

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<<You will need to check the algebra in this carefully>>

Let be the origin , be and be .

Then is .

The slope of is , so the slope of is , in fact

is the line . The line has equation ,

so is the point of intersection of:

,

and

.

Which is the point .

Now lies on , and may be written as for some

.

To finish find the equation on the line through and , and from that

find the coordinates of . Find the slope of the line through and ,

which should be minus the slope of the line through and .

RonL