Q. 295.0( 4 Votes )

Prove that the ta

Answer :

It is given in the question that, O is the centre of the circle and l is the tangent at point A


We have to prove that OA is perpendicular to tangent l


Construction: First of all take a point B on the tangent and join AB. Suppose that OB meets the circle at C


Proof: We know that radius of the circle is equal to each other


OA = OC


Also, OB = OC + BC


Clearly, OB > OC


This will happen with every pint on the line l except the point C also OC is the shortest of all the distances of the point O to the points of tangent (l)


Hence, OC is perpendicular to tangent (l) as we know that the shortest side is the perpendicular


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