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
<Other Science>
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
| 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 |