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Which of the following may fall outside a triangle?
orthocenter and circumcenter
An altitude of a triangle may not fall outside the triangle true or false?
False
Can the median of a triangle fall outside of triangle?
No. It's not possible to start at one vertex of the triangle and proceed to the midpoint of the opposite side, by way of a straight path that takes you outside of the triangle.
How do you find orthocenter?
You find the orthocenter by constructing the altitudes from the vertices in a triangle. If the triangle is obtuse, the orthocenter will fall outside the triangle. If the triangle is acute, the orthocenter will fall on the inside of the triangle. If the triangle is a right triangle, the orthocenter will lie on a vertix.
Is the centroid of a triangle always the circumcenter of a triangle?
No way! An easy example is the centroid and circumcenter of a right-angle triangle. Circumcenter will be exactly on the middle of the hypotenuse which obviously cannot be the centroid. Centroid is the point where all three lines are connecting all the three vertices and the middle of the line opposite the respective vertex. Circumcenter is the center of the circle passing through all the vertices. As it is known, a right-angle triangle will always fall within a semicircle, meaning the circle center will always be on the middle of the hypotenuse.
