Question

Let p1 and p2 be any points on a circle of radius r such that angle p1op2=60 degree.If p is the point of intersection of the two tangents of the circle from p1 and p2 then locus pf p is

Answer 1

hello your answer is p=30

Answer 2

3(x² + y²) = 4r² is Locus of P

Step-by-step explanation:

∠P1OP2 = π/3 = 60°

=> ∠P1OP = 60/2 = 30°

Cos30°  = P1O/OP

=> Cos30° = r / OP

=> OP = r/Cos30°

=> OP = 2r/√3

OP² = (x - 0)²  + (y - 0)²   ( x & y being coordinates of P)

=> x² + y² = 4r²/3

=> 3(x² + y²) = 4r²

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