Q6 of 21 Page 146

The centre of the circle below is the origin and A, B are points on it.


Calculate the length of the chord AB.





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Let coordinates of A be (x1,y1) and coordinates of B be(x2,y2).


Drop a perpendicular from A on X – axis intersecting X axis at P.


Now,


In Δ OPA





And




⇒ x1 = √3


∴ coordinates of A = (√3)


Drop a perpendicular from B on X – axis intersecting X axis at Q.


Now,


In Δ OQB





And





∴ coordinates of B = (– 1,√3)


Hence, length of the chord AB =


The distance between point A and B =



= √8 = √2


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