A tangent to a circle is a line, or a line segment, that touches the circle in exactly one point, and does not pass through the circle. A chord is a line segment connecting two points on a circle. A chord that passes through the center of the circle is a diameter. In this assignment we will discover some facts about chords and tangents.
Problem 1. Draw two circles. In each circle draw a radius and mark the point on the circle that is connected to the center by the radius you drew. Draw a tangent to the circle that passes through this point. What relationship do you see between the tangent line and the radius?
Problem 2. Draw two circles and mark their centers. In each draw a chord and then draw the perpendicular bisector of the chord. What do you notice about the relationship between the bisector and the center?
Problem 3. Use what you discovered in Problem 2 to find a procedure that, given a circle, will determine the center of the circle without needing to approximate or guess its location, and without measuring anything. (Hint: if we have worked Drawing Circles Through Points, what we did in that assignment may help you find the procedure.)