The tangent at any point of a circle is perpendicular to the radius th

1.	The tangent at any point of a circle is perpendicular to the radius the point of contact
Answer» Let APB be the tangent and take O as centre of the circle.Let us suppose that MP{tex}\\bot{/tex}AB does not pass through the centre.Then,{tex}\\angle OPA = 90^\\circ{/tex} [{tex}\\because{/tex} Tangent is perpendicular to the radius of circle]But {tex}\\angle MPA = 90^\\circ{/tex} [Given]{tex}\\therefore \\angle OPA = \\angle MPA{/tex}This is only possible when point O and point M coincide with each other.Hence, the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

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