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Standard XII

Mathematics

Properties of Radical Axis

Circles are d...

Question

Circles are drawn through the points $(a, b)$ and $(b, - a)$ such that common chord substend an angle of $45 °$ on the circumference on any of the circles. If distance between the centres is $\sqrt{k}$ times the radius of the smaller circle , then $k =$

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Solution

$∵$ common chord substend an angle of $45 °$ on the circumference
$∴$ angle made by the same chord to centre of any circle will be $90 °$ and radii of both the circles will be same

Hence we can say that both the circles will be orthogonal to eachother
$∴$ distance between the centres $= \sqrt{2}$ radius
$\Rightarrow k = 2$

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Circles are drawn through the points (a,b) and (b,−a) such that common chord substend an angle of 45° on the circumference on any of the circles. If distance between the centres is √k times the radius of the smaller circle , then k=

Circles are drawn through the points $(a, b)$ and $(b, - a)$ such that common chord substend an angle of $45 °$ on the circumference on any of the circles. If distance between the centres is $\sqrt{k}$ times the radius of the smaller circle , then $k =$