四点共圆判定（The four point circle criterion）.docVIP

四点共圆判定（The four point circle criterion） To prove the basic circle four point method: Methods 1 From card round total of four points in the first selected three point as a circle, and then another card in this circle, if we can prove this point, can be sure that this round total of four points. Methods 2 The four point circle into two triangles is the bottom edge of the triangle, and two in the bottom of the same side, if you can prove that the angles are equal (the same circumference of the arc angle, which can be sure that this is equal) round total of four points. (if you can prove that the two vertex is a right angle. You can sure these four points were round, and two points for the hypoteneuse diameter). Methods 3 The common round four points into quadrilateral, if we can prove the diagonal complementary or that one of its corners in the diagonal equal to its adjacent supplementary, can be sure that this round total of four points. Methods 4 The two lines are common round four point two two into the intersection, if they can prove their intersection is divided into two segments by the product of equal, can be sure that this round total of four points (inverse theorem of intersecting chords theorem); or to be common round four point two two link and the extension of the intersection of two lines, if they can prove self to a line two points into two segments of the product is equal to two points to another intersection line segments into two segments of the product, can be sure this four point circle. (inverse theorem of secant theorem) Methods 5 Is card circle point to a certain point distance is equal, so as to determine their circle. Both are quadrilateral three sides perpendicular bisector intersection, can be sure that this round total of four points. The five basic methods in each according to four points of a circle is a reason, so when the request card round total of four points when the problem, we must first according to the conditions of the proposition