Prove that the angle between two tangents drawn from an external point to a circle is supplementary to the angle - Maths - Circles

Question

Prove that the angle between two tangents drawn from an
external point to a circle is
supplementary to the angle subtended by the line segment
joining the points of contact at the centre

Vishal Hans · Accepted Answer

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To prove :-
1+2 = 180 degree
proof :-
since 3=4= 90 degree ( line from centre is perpendicular to the
tangent at the pt of contact)
1+2+3+4 = 360 ( A S P of quadrilateral)
1 +2+ 180 degree = 360 dergree
1+2= 180 degree
hence proved

. Prove that the angle between two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

. Prove that the angle between two tangents drawn from an external point to a circle is

supplementary to the angle subtended by the line segment joining the points of contact at the centre.