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Angle between tangentsdrawn from a point p to circle x2+y2-4x-8y+8=0 is 60then length of chord of contact of p is
4 months ago

This is a simple question if you know some properties of circle.
I can’t explain it diagrammatically here. Please understand. I’ve explained it fully.

Let the centre of circle be O and tangents from P meet the circle at Q and R. Let M be the point of
intersection of QR and OP. Then QR is the chord of contact of P.

Radius of circle, r = = = = 2
We know at the point of contact, radius of circle is perpendicular to tangent.
So, OQP = ORP = 90.
Also, QR is perpendicular to OP i.e. OMQ = 90.

OP bisects QPR  i.e.  QPO = RPO = 30.
QOP = 60.
QM = OQsin60 = rsin60 = 2.( / 2) = 3.
OP bisects QR i.e. QM = MR  or
QR = 2.QM = 2.3  =  6 unit = length of chord of contact of P.
4 months ago
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