If z_1, z_2, z_3 are the vertices of an equil | vedclass

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(A) Given that $z_1, z_2, z_3$ are the vertices of an equilateral triangle and $z$ is its circumcentre.Since $z$ is the circumcentre,the distance from

Vedclass · Accepted Answer

$\frac{|z-z_1|}{|z-z_2|} = \frac{|z-z_3|}{|z-z_1|}$

Vedclass · Answer

(A) Given that $z_1, z_2, z_3$ are the vertices of an equilateral triangle and $z$ is its circumcentre.Since $z$ is the circumcentre,the distance from $z$ to each vertex is equal to the circumradius $R$.Therefore,$|z-z_1| = |z-z_2| = |z-z_3| = R$.Now,consider the ratio $\frac{|z-z_1|}{|z-z_2|} = \frac{R}{R} = 1$.Also,$\frac{|z-z_3|}{|z-z_1|} = \frac{R}{R} = 1$.Thus,$\frac{|z-z_1|}{|z-z_2|} = \frac{|z-z_3|}{|z-z_1|} = 1$.

If $z_1, z_2, z_3$ are the vertices of an equilateral triangle and $z$ is its circumcentre,then

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