Question

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​

Answer 1

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​.