Question

prove that the tangent at any point of a circle is perpendicular to the Radius through the point of contact​

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Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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Referring to the figure:

OA=OC (Radii of circle)

Now OB=OC+BC

∴OB>OC (OC being radius and B any point on tangent)

⇒OA<OB

B is an arbitrary point on the tangent.

Thus, OA is shorter than any other line segment joining O to any

point on tangent.

Shortest distance of a point from a given line is the perpendicular distance from that line.

Hence, the tangent at any point of circle is perpendicular to the radius.

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Answer 2

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