Question

A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle can not be

• A. 1
• B. 2
• C. $\frac { 3 } { 2 }$
• D. 4

Answer 1

Answer: (D)

4

Answer 2

Let the vertices of the triangle be (cos q_i, sin q_i),

i = 1, 2, 3

Ž orthocentre is ((cosq₁ + cos q₂ + cos q₃),

(sin q₁ + sinq₂ + sinq₃))

Ž distance between the orthocentre and the circumcentre is

$\sqrt { \left( \cos \theta _ { 1 } + \cos \theta _ { 2 } + \cos \theta _ { 3 } \right) ^ { 2 } + \left( \sin \theta _ { 1 } + \sin \theta _ { 2 } + \sin \theta _ { 3 } \right) ^ { 2 } }$

< 3.