."l capmJgiH+:Hn:y):u@a8HـA\|u@aLHA8!|aN |!~&'OzBk 9_ /W]Looking at four centers of triangles. Centroid G is constructed from the point of intersection of the segments that extend from a vertex to the midpoint of the opposite side. The centroid always stays inside the triangle. Orthocenter H is constructed by finding the point of intersection of altitudes dropped from each of the 3 vertices. The orthocenter exits the triangle as soon as it becomes obtuse. The circumcenter C is found by getting the point of intersection of the perpendicular bisectors of each side of the triangle. It is the center of a circle that circumscribes the triangle. The circumcenter also exits the triangle when it becomes obtuse. Incenter I is found by locating the intersection of the angle bisectors of each of the vertices. It is the center of a circle that inscribes the triangle and never exits the triangles sides.ides.s.s.s.s.des.s.s.s.(AH`|}xd,@|8aLH`xxH`;H{::y):oUhob{ E#o S When all four of these centers are constructed within a single triangle, it is interesting to note the relationship they have to each other and the triangle as the triangle changes shape. When the triangle is equilateral, all four points are the same. When the triangle is obtuse, H and C exit the triangle while G and I stay within the triangle sides. When the triangle is right, C rests on the right vertex and H lies at the midpoint of the hypotenuse. When the triangle is isosceles, all the points rest in a line with C and H on opposite ends of the line. When a vertex is opened to 180 degrees, center I rests on the vertex and G not too far away. when it becomes obtuse. Incenter I is found by locating the intersection of the angle bisectors of$)x :y):CEDBdA.@!K?HP 7Cl 7C,l 7C|CB  Hh] :y):B7C<7Cl 7XZ6  |D)C @ :y):Ad7C4  c1|CC   :y):rp5 c1'|CCC.C?o ?I  :y):q'(z~z~#oC:\WIN98\EXPLO|D)CD[C|u:?# 7L  :y):lI:D Ilh7C7C7CL7C7C7C7C|CBD)C?#  :y):kt 7C   a4|CCCB?  :y):jnCCCA0AXZ?PH7Cd7C4d7C|D)CCC?@E :y):I A|DC  :y):HP @ |C܀Co ]b  :y):Ghh|D@C  :y):I '?'? wּw|D9Cr U'  :y):oI?CmC L D7CD7C7CD7C!|CCaD[C? =&' :y):n G'|DCCD?   :y):y=nl,DC  xIIf|D)CC܀Co? Ed  :y):xd_Text.charAt(; |CCDC? j' :y):v9CC pI|CpCJD C? ' :y):tI7E<J B|DCCCV? fk :y):H h'?'? wVw|DCz    :y):G'?'? wּw|DCv  :y):C h'?'? wVw|CqCt