![]() Īny two circles with the same radius are congruent− if one circle is moved so that its centre coincides with the centre of the other circle, then it follows from the definition that the two circles will coincide. The plane has this property except for lines.ĮXERCISE 1 a Identify all translations, rotations and reflections of the plane that map a line onto itself.ī Which of the transformations in part a map a particular point P on to another particular point Q on. ![]() The same as every other point on the circle − no other figure in Thus every point on a circle is essentially It can also be done by a reflection in the diameterĪOB bisecting POQ. This canīe done by a rotation through the angle θ = POQ about Thus every diameter of the circle is an axis of symmetry.Īs a result of these symmetries, any point P on a circleĬan be moved to any other point Q on the circle. Reflection in the line AOB reflects the circle onto itself. If AOB is a diameter of a circle with centre O, then the.A circle has every possible rotation symmetry about its centre, in that every rotation of the circle about its.Thus a chord is the interval that the circle cuts off a secant, and a diameter is the interval cut off by a secant passing through the centre of a circle centre. A line that cuts a circle at two distinct points is called a secant.The word ‘diameter’ is use to refer both to these intervals and to their common length. Since a diameter consists of two radii joined at their endpoints, every diameter has length equal to twice the radius. A chord that passes through the centre is called a diameter.An interval joining two points on the circle is called a chord. ![]() Notice that the word ‘radius’ is being used to refer both to these intervals and to the common length of these intervals. By the definition of a circle, any two radii have the same length.
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