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Grade 11Discuss with colleagues and IITians

The sides of triangle are Ur = Xcos Ar + ysinAr – Pr =0 , (R = 1,2,3) . Show that orthocentre is given by U1 cos(A2 – A3) = U2cos(A3 – A1) = U3cos(A1 – A2)

muktesh singh

11 Years agoGrade 11

1 Answer

Arun

6 Years ago

Any line through the intersection of lines L

1

and L

2

and perpendicular to L

3

is

cosα

1

cosα

3

+sinα

1

sinα

3

L

1

=

cosα

2

cosα

3

+sinα

2

sinα

3

L

2

L

1

cos(α

2

−α

3

)=L

2

cos(α

3

−α

1

)=L

3

cos(α

1

−α

2

) by symmetry

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