please help here :
Prove that the orthocentre of a triangle ABC with A(x1,y1), B(x2,y2) and C(x3,y3) is

(x1 tan A + x2 tan B + x3 tan C)/(tan A + tan B + tan C), (y1 tan A + y2 tan B + y3 tan C)/(tan A + tan B + tan C)

Question

please help here :
Prove that the orthocentre of a triangle ABC with A(x1,y1), B(x2,y2) and C(x3,y3) is 

(x1 tan A + x2 tan B + x3 tan C)/(tan A + tan B + tan C), (y1 tan A + y2 tan B + y3 tan C)/(tan A + tan B + tan C)

mathslover · Answer

@amistre64

mathslover · Answer

@AravindG

amistre64 · Answer

that looks hideous

aravindg · Answer

yep it seems to be :P

amistre64 · Answer

orthocenter is where the bisectors cross right?

aravindg · Answer

i bet we need to bring right angle triangles oout of the bisectors ,express tan using the angles and get to the result

aravindg · Answer

@mathslover  what was ur attempt on this qn?

mathslover · Answer

one minute @AravindG

amistre64 · Answer

crossing alts ... not bisectors

mathslover · Answer

i and another user did this ... but we can not proceed further

amistre64 · Answer

the setup seems to follow a pattern that only differs by xs and ys

mathslover · Answer

yes a symmetric case

aravindg · Answer

do u have the book arihant trigonometry ?this qn is answered in that book

mathslover · Answer

no @AravindG  can u upload the screenshot of that answer please @AravindG

ganpat · Answer

@mathslover : Thats the solution in your attachment.. As you found for point D, Apply the same formula for the point O , such that Point O is on the line A and D.. 

Do not go for E and any other point.

mathslover · Answer

@amistre64 and @Ganpat can u tell me that how to apply the same formula for the point O ?