Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Given that: ACB is an arc of the circle with center O, C is the midpoint of arc ACB. Line PQ is the tangent to the circle passing at point C. AB is the chord joining the endpoints A and B of arc. OA=OB (Radii of a circle). Draw a perpendicular bisector of chord AB. Bisector line passes through point C and center O. OC is perpendicular to AB. PQ is a tangent at the point C, then it is also perpendicular to OC. Hence, both lines AB and PQ are perpendicular to OC. Therefore, the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the endpoints of the arc.