Location of the Circumcenter: The circumcenter is not always located inside the triangle. The location of the circumcenter depends on the type of triangle that we have. Acute Triangle: Right Triangle: Obtuse Triangle: The circumcenter is located The circumcenter is located The circumcenter is located ____________________the triangle. _______ the right angle. _________________________ the triangle. Properties of the Circumcenter: The circumcenter is the center of the circle that can be circumscribed around the triangle. Example: Examples: The perpendicular bisectors of intersect at point If = 20 and = , then what is the value of P. A P BP x? ΔABC The perpendicular bisectors of intersect at point = , = 10, and = . Find and P. AP BP CP x y. ΔABC The perpendicular bisectors of are concurrent at = , = and = 12. Find and P. AP BP CP x y. ΔABC
Location of the Circumcenter: The circumcenter is not always located inside the triangle. The location of the circumcenter depends on the type of triangle that we have. Acute Triangle: Right Triangle: Obtuse Triangle: The circumcenter is located The circumcenter is located The circumcenter is located ____________________the triangle. _______ the right angle. _________________________ the triangle. Properties of the Circumcenter: The circumcenter is the center of the circle that can be circumscribed around the triangle. Example: Examples: The perpendicular bisectors of ΔABC intersect at point P. If A P = 20 and BP = , then what is the value of x? The perpendicular bisectors of ΔABC intersect at point P. AP = , BP = 10, and CP = . Find x and y. The perpendicular bisectors of ΔABC are concurrent at P. AP = , BP = and CP = 12. Find x and y.