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Question
In Q.No. 1, write the distance between the circumcentre and orthocentre of ∆OAB.
Solution
The coordinates of circumcentre of a triangle are the point of intersection of perpendicular bisectors of any two sides of the triangle.
Thus, the coordinates of the circumcentre of triangle OAB is \[\left( \frac{a}{2}, \frac{b}{2} \right)\], as shown in the figure.
We know that the orthocentre of a triangle is the intersection of any two altitudes of the triangle.
So, the orthocentre of triangle OAB is the origin O(0, 0).
\[\therefore\] Distance between the circumcentre and orthocentre of ∆OAB = OC
\[\Rightarrow OC = \sqrt{\left( \frac{a}{2} - 0 \right)^2 + \left( \frac{b}{2} - 0 \right)^2} = \frac{\sqrt{a^2 + b^2}}{2}\]
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