A) \[\frac{1}{2}\]
B) \[2\]
C) \[\frac{3}{2}\]
D) \[4\]
Correct Answer: D
Solution :
[d] Let the vertices of the triangle be \[(\cos \,{{\theta }_{i}},\,\,\sin {{\theta }_{i}}),\]\[i=1,2,3\]. \[\therefore \] Circumcentre\[\equiv \,\,\,\,(0,0)\] Also, orthocentre is \[((\cos {{\theta }_{1}}+\cos {{\theta }_{2}}+\cos {{\theta }_{3}}).\] \[(\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}}))\] \[\Rightarrow \] Distance between orthocentre and circumcentre \[=\sqrt{{{(\cos {{\theta }_{1}}+\cos {{\theta }_{2}}+\cos {{\theta }_{3}})}^{2}}+{{(\sin {{\theta }_{1}}+\sin {{\theta }_{2}}+\sin {{\theta }_{3}})}^{2}}}<3\]
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