$I n Q > N o .1, Write the distance between the circumcentre and orthocentre of Δ O A B .$

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Solution

$Point of intersection of altitudes from vertices A and B of triangle is O(0,0) \Rightarrow Orthocentre of triangle is O (0,0) Let,P(x,y)be the circumcentre of triangle \Rightarrow O P = A P = B P O P^{2} = A P^{2} x^{2} + y^{2} = (x - a)^{2} + y^{2} \Rightarrow x^{2} = x^{2} - 2 a x + a^{2} \Rightarrow a^{2} = 2 a x x = \frac{a}{2} a n d O P^{2} = B P^{2} x^{2} + y^{2} = (x - 0)^{2} + (y - b)^{2} x^{2} + y^{2} = x^{2} + y^{2} - 2 b y + b^{2} \Rightarrow b^{2} = 2 b y \Rightarrow y = \frac{b}{2} S o, c i r c u m c e n t r e = p (\frac{a}{2}, \frac{b}{2}) Distance between orthocentre O(0,0)~and c i r c u m c e n t r e p (\frac{a}{2}, \frac{b}{2}) i s = \sqrt{{(\frac{a}{2})}^{2} + {(\frac{b}{2})}^{2}} R e q u i r e d d i s t a n c e = \frac{1}{2} \sqrt{a^{2} + b^{2}} u n i t s .$

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In Q>No.1,Write the distance between the circumcentre and orthocentre ofΔOAB.

$I n Q > N o .1, Write the distance between the circumcentre and orthocentre of Δ O A B .$