Question

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

Answer 1

Answer:

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.

solution

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Answer 2

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