Prove that the perpendicular at the point of contact to tangent to a circle passes through centre.

line  l is tgt to the circleat P. O is the centre of the circle.OP=radius of the circle.If we hav some points Q1,Q2  etc. on l then we find that OP is the shorter distance from O in comparison to the distance OQ!,OQ2,etc. There fore OP is perpendicular to  l. Hence the perpendicular OP drawn to the tangentline at P passes through the centre O of the circle.