Question

prove that the tangent of circle is perpendicular to radius through the pont of contact. (with diagram )​

Answer 1

Answer:

Let O be the centre of the circle, let ℓ be a tangent line, and let P be the point of tangency. ... Draw the line through O which is perpendicular to ℓ. Then this line meets ℓ at a point Q≠P. Note that Q is outside the circle.

Answer 2

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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.