orthocenter - 2024 ACF Fall

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


Cornell G	Binghamton A	0	0	10	10
Binghamton B	U of Rochester A	0	0	10	10
Binghamton C	RIT B	0	0	10	10
Penn State	Cornell C	0	0	10	10
RIT C	Cornell D	0	0	10	10
Cornell E	RIT A	0	10	10	20
ESF	Cornell A	0	0	10	10
Auburn A	Clemson B	0	0	10	10
Auburn B	Vanderbilt A	0	0	10	10
Emory A	Belmont	0	0	10	10
Auburn C	Clemson A	0	0	10	10
Georgia Tech E	Furman	0	0	10	10
Georgia Tech A	Georgia A	0	0	10	10
Claremont A	Claremont B	10	0	10	20
Claremont C	USC	10	10	10	30
UCLA B	UCLA A	10	0	10	20
UCLA D	UCLA C	0	0	10	10
UCLA E	UCSD	10	10	10	30
SIUE	Chicago A	0	0	10	10
Cornell B	Syracuse	0	0	10	10
U of Rochester B	Cornell F	0	0	10	10
West Virginia B (UG)	CWRU C (UG)	0	0	0	0
Miami C (DII)	Michigan C	0	0	0	0
Miami A (UG)	Michigan A (UG)	0	0	10	10
Michigan State A	CWRU A (UG)	10	0	10	20
Ohio State B (DII)	Jefferson County Scholars (DII)	10	10	10	30
Emory Oxford	South Carolina A	10	0	10	20
South Carolina B	Alabama A	0	0	10	10
Southern	Tennessee A	0	0	10	10
Georgia Tech C	Tennessee B	10	0	10	20
Georgia Tech D	Vanderbilt B	10	0	10	20
Lehigh B (DII)	Rowan A (DII)	0	0	10	10
Lehigh A (UG)	Maryland A (DII)	0	0	10	10
Maryland B (DII)	Penn B (DII)	10	0	10	20
Columbia A (UG)	Princeton A (UG)	10	0	10	20
Miami B (UG)	Michigan State B	0	0	10	10
CWRU B (DII)	Ohio State A (UG)	10	0	10	20
Michigan D (UG)	Ohio State C (DII)	10	0	10	20
UW Gluttony	Arizona State B	0	0	10	10
UBC B	UW Chastity	0	0	10	10
UBC A	UW Envy	10	0	10	20
UW Greed	Arizona State A	0	0	10	10
UW Lust	UW Sloth	0	0	10	10
UW Wrath	Boise State	0	0	10	10
Appalachian State B	Liberty A	0	0	10	10
Appalachian State A	Duke B	10	0	10	20
NC State	James Madison A	0	0	10	10
NC State	James Madison A	0	0	10	10
NC State	James Madison A	0	0	10	10
NC State	James Madison A	0	0	10	10
NC State	James Madison A	0	0	10	10
NC State	James Madison A	0	0	10	10
NC State	James Madison A	0	0	10	10
NC State	James Madison A	0	0	10	10
Liberty B	UNC D	0	0	10	10
Virginia	Liberty C	0	0	10	10
VCU	Tusculum	0	0	10	10
William & Mary	UNC B	10	0	10	20
James Madison B	UNC C	0	0	10	10
Virginia Tech B	UNC A	0	0	10	10
Fordham A	Bard A (UG)	10	0	10	20
NYU B	Columbia B	0	0	10	10
NYU A (UG)	Rutgers A (UG)	0	0	10	10
Penn A (DII)	Rutgers B	10	10	10	30
Iowa B	Chicago B	0	0	10	10
Purdue B	Illinois A	0	0	10	10
Notre Dame C	Illinois B	0	0	10	10
Illinois D	Purdue A	0	0	10	10
Notre Dame A	Indiana	10	0	10	20
Northwestern B	Purdue C	10	0	10	20
Notre Dame B	WashU A	0	0	10	10
Northwestern A	WashU B	10	0	10	20