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

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\* herefore OB>OC;;;;;(OC ;being; radius ;and B; any ;point; on; tangent)\* Rightarrow 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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Deependra Verma

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