orthocenter - 2024 ACF Fall at Washington

Question

This point lies inside a triangle if and only if all of its angles are acute. For 10 points each:

[10m] Name this point denoted “H” that is found at the intersection of the three altitudes of a triangle.

ANSWER: orthocenter

[10h] Along with the centroid and circumcenter, the orthocenter is used to define this construct. This construct is ill-defined for equilateral triangles because all three points coincide.

ANSWER: Euler line

[10e] The Euler line coincides with the line of symmetry in these triangles, which have exactly two sides with the same length.

ANSWER: isosceles triangles

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Summary


2024 ACF Fall at Cornell	fall	Y	9	11.11	100%	0%	11%
2024 ACF Fall at Ohio State	fall	Y	8	13.75	75%	50%	13%
2024 ACF Fall at Washington	fall	Y	6	11.67	100%	17%	0%
2024 ACF Fall at Georgia	fall	Y	11	12.73	100%	27%	0%
2024 ACF Fall at North Carolina	fall	Y	10	12.00	100%	20%	0%
2024 ACF Fall at Claremont Colleges	fall	Y	5	22.00	100%	80%	40%
2024 ACF Fall at Rutgers	fall	Y	8	16.25	100%	50%	13%
2024 ACF Fall at Illinois	fall	Y	9	13.33	100%	33%	0%

Data


UW Gluttony	Arizona State B	0	10	10
UBC B	UW Chastity	0	10	10
UBC A	UW Envy	10	10	20
UW Greed	Arizona State A	0	10	10
UW Lust	UW Sloth	0	10	10
UW Wrath	Boise State	0	10	10