Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
12/9/2012 Theorem The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the th vertices ti B Diagram Symbols Perpendicular bisectors A PX , PY , and PZ are concurrent at P. X Y PA = PB = PC P Z C 1 12/9/2012 When 3 or more lines intersect at one point, they are concurrent. The point at which they intersect is the point of concurrency. The point of concurrency of the perpendicular bisectors of a triangle is called the circumcenter of the triangle. Since the circumcenter is equidistant from the vertices you can use the circumcenter as the vertices, center of the circle that contains each vertex of the triangle. You say the circle is circumscribed about the triangle. A X Y P B Z C 2 12/9/2012 Find the circumcenter of the following 3 points. Circumcenter Theorem The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle. Diagram Symbols Angle bisectors AP, BP, and CP A are concurrent at P. PX = PY = PZ X Y P B Z C 3 12/9/2012 The point of concurrency of the angle bisectors of a triangle is called the incenter of the triangle. P is the center of the circle that is inscribed in the triangle. A X Y P B C Z If P is the incenter and PY = 2x-4 and PZ = 5x-13, find BP, if PB = 3x. 2 x − 4 = 5 x − 13 9 = 3x A PB = 3(3) X 3x 3= x Y P PB = 9 2x-4 5x-13 B Z C 4 12/9/2012 P. 305 #’s 8-12 even, 15-18, 22, 33-34, 37-40 5