Question

B Activity: x Draw a sufficiently large circle with centre 0. Draw radius OP. Draw a line AB I seg OP. It intersects the circle at O A points A, B. Imagine the line slides towards point P such that all the time it remains parallel to its original position. Obviously, while the line slides, points P A and B approach each other along the Fig. 3.9 circle. At the end, they get merged in point P, but the angle between the radius OP line AB will remain a right angle. At this stage the line AB becomes a tangent of the circle at P. So it is clear that, the tangent at any point of a circle is perpendicular to the radi at that point. This property is known as 'tangent theorem'. ​

Answer 1

parallel to its original position. Obviously, while the line slides, points P A and B approach each other along the Fig. 3.9 circle. At the end, they get merged in point P, but the angle between the radius OP line AB will remain a right angle. At this stage the line AB becomes a tangent of the circle at P. So it is clear that, the tangent at any point of a circle is perpendicular to the radi at that point. This property is known as 'tangent theorem