In Q.No. 1, write the distance between the circumcentre and orthocentre of ∆OAB.

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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 $(\frac{a}{2}, \frac{b}{2})$ ,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).

$∴$ Distance between the circumcentre and orthocentre of ∆OAB = OC

$\Rightarrow O C = \sqrt{{(\frac{a}{2} - 0)}^{2} + {(\frac{b}{2} - 0)}^{2}} = \frac{\sqrt{a^{2} + b^{2}}}{2}$

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