CircleHard

Question

Lines L1 : x + y = 2 and L2 : y -(2 + √3)x + (1 + √3) = 0 intersect circle S1 = 0 (radius r) at A,B and A,C respectively such that AB = AC = 10 and L3 = 0 is equation of tangent at point A of circle S1 = 0, then -

Options

A.r can be
B.r can be 10
C.L3 = 0 can be y + (2 + √3)x - √3(1 + √3) = 0
D.L3 = 0 can be x - y(2 + √3) +(1 + √3) = 0

Solution

           
Angle between lines L1 & L2 is given by
tan θ =
⇒ θ =
cos 30o = or cos 60o =
⇒ r = or r = 10
tangent at point A are lines along angle bisectors of L1 & L2

x + y - 2 = ±
(√3 + 1)(x + y - 2) = ±(y - (2 + √3)x + 1 + √3)

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