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)

Create a free account to view solution

View Solution Free
Topic: Circle·Practice all Circle questions

More Circle Questions

The number of common tangents to the circlex2 + y2 - 4x - 6y - 12 = 0 andx2 + y2 + 6x + 18y + 26 = 0, is :...If the circle x2 + y2 = a2 cuts off a chord of length 2b from the line y = mx + c, then-...A circle touches a straight line lx + my + n = 0 and cuts the circle x2 + y2 = 9 orthogonally. The locus of centres of s...Two lines through (2, 3) from which the circle x2 + y2 = 25 intercepts chords of length 8 units have equations...Six boy and six girls sit along a line alternatively with probability P1 and along a circle (again alternatively) with p...