prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the point of contact at the centre
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Answer:we know that tangents are perpendicular to the point of contact with the radius.
therefore angle ABO=angle ACO=90 degree.
now in quadrilateral ABOC angle ABO+angle BOC+angle OCA+angle CAO=360 degree
90+y+90+x=360 degree
=>x+y=360-180 degree=180 degree
therefore,the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the point of contact at the centre.
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