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

Posted by Rishi Ojha Ojha 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

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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CBSE > Class 10 > Mathematics