Circle - Tangent at every point is perpendicular to the Radius
Another property we find related to circles is the tangent at any point on a circle is always perpendicular to the radius at that point. Remember that tangent to a circle is a line that intersects the circle at one and only one point. You can take any point on a circle and draw the tangent at that point, the corresponding radius at that point will always be at right angle with the tangent. ‘Proof by contradiction’ is usually the method used to prove this statement. In this method, we first assume that our statement is not true, i.e, we assume that in a circle the radius is never perpendicular to the tangent. We then use some mathematical results which will eventually lead us to contradiction. Contradiction means something like “night and day occurring at the same time”, or “x is both bigger and smaller than y(x > y & x < y)”. Arriving at some sort of contradiction would imply that our initial assumption that radius is not perpendicular to the tangent wa...