Understand a figure which consists of a set of the points of the plane equidistanted from its center as a circle. The distance from the center to points of a circle is called radius.
It is required to you
- - simple pencil;
- - notebook;
- - protractor;
- - compasses;
- - handle.
Instruction
1. Before finding that coordinate or other point of a circle, construct the set circle. At its construction to you a set of new concepts can meet. So the chord is a piece which connects two points of a circle, and the chord passing through the center of a circle - maximum (it carries the name of diameter). Besides, to a circle the tangent which represents the straight line perpendicularly located to the circle radius which is carried out to a point of intersection of a tangent and the considered geometrical figure can be carried out.
2. If on a condition of a task it is known that the circle constructed by you is crossed by other circle (it less by the sizes), represent it graphically: in the drawing it has to be represented that two of these circles are crossed, that is have a number of the general points. Designate the center of the first circle by a point 1 (its coordinates (X1,Y1)), and its radius - R1. Thus, the center of the second circle has to be designated by a point 2 (coordinates of this point (X2,Y2)), and radius - R2. Put the end to points of intersection of figures 3 (X3,Y3) and 4 (X4,Y4). The central point of intersection has to be designated by 0: its coordinates (X, Y).
3. To find coordinates of suppression of these circles and consequently also the point belonging to both the first, and the second of them you should solve a quadratic equation. Consider two formed triangles (? 103 and? 203) also analyze their indicators. Hypotenuses of these triangles there is R1 and R2 respectively. Knowing value of hypotenuses, find the piece of D connecting the center of the first circle to the center of the second. The chosen calculation method directly depends on what the triangles analyzed by you turned out. If they rectangular, then the square of length of a hypotenuse of each of them is equal to the sum of squares of legs of this triangle. Besides, length of a leg can be found on a formula: = ccos?, where with – the hypotenuse length, and cos? – cosine of an adjacent corner. Having found value of legs, determine coordinates of the point interesting you.