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

Asked by Anjana | 2nd Mar, 2019, 03:38: PM

Expert Answer:

Draw a circle with centre O
tangent at P 
now XP is drawn perpendicular to Tangent t at P
also, we know that OP is perpendicular to tangent t, due to the tangent radius relation
now by the uniqueness of perpendicular, we can draw only one perpendicular to t at point P
so X and O is on the same line
the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Answered by Arun | 2nd Mar, 2019, 05:47: PM