prove the statement below
"the tabgent at any point of a circle is perpendicular to the radius through the point of contact"
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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.
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why re axam he kyaa
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