prove that the tangent of a circle at any joint on its perpendicular to the radius passes through the point of contact.
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Proof: We know that, among all line segment joining the point O to a point on l, the perpendicular is shortest to l. Now, OB = OC + BC. B is an arbitrary point on the tangent l. Thus, OA is shorter than any other line segment joining O to any point on l.
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