If from any point on the circle x 2 +y 2 +2gx+2fy+c=0 tangents are drawn to the circle x 2 +y 2 +2gx+2fy+csin 2 α+(g 2 +f 2 )cos 2 α=0,show that the angle between the tangents is equal to 2α.

Question

If from any point on the circle x 2 +y 2 +2gx+2fy+c=0 tangents are drawn to the circle x 2 +y 2 +2gx+2fy+csin 2 &alpha;+(g 2 +f 2 )cos 2 &alpha;=0,show that the angle between the tangents is equal to 2&alpha;.

Archit Bhatt · Answer

its very easy..take the ratio of the radii....join the points from which tangents are drawn 2 d center of the circle...n let the angle b theta betn d line joinin d centers and the tangent u will find that theta equals alfa n then twice d angle will be d angle betn the tangents => 2 alfa

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If from any point on the circle x 2 +y 2 +2gx+2fy+c=0 tangents are drawn to the circle x 2 +y 2 +2gx+2fy+csin 2 α+(g 2 +f 2 )cos 2 α=0,show that the angle between the tangents is equal to 2α.

If from any point on the circle x²+y²+2gx+2fy+c=0 tangents are drawn to the circle x²+y²+2gx+2fy+csin²α+(g²+f²)cos²α=0,show that the angle between the tangents is equal to 2α.

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If from any point on the circle x 2 +y 2 +2gx+2fy+c=0 tangents are drawn to the circle x 2 +y 2 +2gx+2fy+csin 2 α+(g 2 +f 2 )cos 2 α=0,show that the angle between the tangents is equal to 2α.

If from any point on the circle x2+y2+2gx+2fy+c=0 tangents are drawn to the circle x2+y2+2gx+2fy+csin2α+(g2+f2)cos2α=0,show that the angle between the tangents is equal to 2α.

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If from any point on the circle x²+y²+2gx+2fy+c=0 tangents are drawn to the circle x²+y²+2gx+2fy+csin²α+(g²+f²)cos²α=0,show that the angle between the tangents is equal to 2α.