If we cut a circle of radius r at a point and form a line out of it, the length of the line is
segment
arc
circumference
If we cut a circle of radius r at a point and form a line out of it, the circumference of the circle becomes the length of the line, which is 2πr.
In the circle centred at O, the tangents at A and B intersect at P. Prove the following:
(i)
the point P is equidistant from A and B
(ii)
the line OP bisects the line AB and the angle APB
(iii)
if the line OP cuts the line AB at Q, then OQ × OP = r2, where r is the radius of the circle