Q24 of 47 Page 1

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


Let there be a circle with center O and radius OP and let Point P be the point of contact of the tangent


Let T be any variable point on the tangent


Distance OT = OQ + QT where OQ is a constant length and QT a variable length


From our concepts of Coordinate Geometry, we know distance between a line and a point is minimum when we consider the perpendicular distance between them


So minimum distance of OT occurs when the variable length QT is 0


OT = OQ = OP (Radius of circle)


Since the minimum distance between a tangent and a point is the perpendicular distance between them, hence the tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.


Answer: Proved


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