Question
A chord, at a distance of 1 unit from the centre, has a
length equal to k² sin (π/4) and the radius of the circle is (-k) sin(π/3). What is the value of k, if k is an integer?Solution
Radius = (-k) sin(π/3) = -√3k/2 Distance from chord to centre = OM = 1unit MR = length of chord/2 = [k2sin(π/3)]/2 = k2/2√2 In triangle OMR, => OM2 + MR2 = OR2 ⇒ 1 + k4/8 = 3k2/4 ⇒ k4 - 6k2 + 8 = 0 By hit and trial method, we get k = -2
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