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Two variable chords A Ba n dB C of a cir...

Two variable chords `A Ba n dB C` of a circle `x^2+y^2=r^2` are such that `A B=B C=r` . Find the locus of the point of intersection of tangents at `Aa n dCdot`

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The correct Answer is:
`x^(2)+y^(2)=4r^(2)`
Let the point of intersection of tangents at A and be `P -= (x,y)` .
Since `AB =AO =BO =r`, we get
`/_ AOB =60^(@)`

or `(PA)/(r) tan 60^(@) = sqrt (3)`
or `sqrt(x^(2)+y^(2)-r^(2))=sqrt(3)r`
Therefore, `x^(2)+y^(2)=4r^(2)` is the locus of the point P.
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