Question

The orthocentre of the triangle formed by the points A(a cos $\alpha$ ,a sin $\alpha$) $B (a \, \cos \, \beta , a\, \sin \, \beta) \, C ( a \, \cos \, \gamma , a \, \sin \, \gamma) $ is

• A. $(cos \, \alpha + cos \, \beta + cos \, \gamma , sin \, \alpha + sin \, \beta + sin \, \gamma )$
• B. $[a(cos \, \alpha + cos \, \beta + cos \, \gamma ),a( sin \, \alpha + sin \, \beta + sin \, \gamma )]$
• C. $[a(cos \, \alpha + sin \, \beta + sin \, \gamma ),a( sin \, \alpha +cos \, \beta + sin \, \gamma )]$
• D. $(cos \, \alpha \: cos \, \beta \: cos \, \gamma , sin \, \alpha \:sin \, \beta \:sin \, \gamma )$

Answer 1

Answer: (B)

Circum center (0,0)
Ortho center = $(x_1 +x_2 +x_3, y_1 + y_2 -y_3)$