Let $ABC$ be a right triangle at $A$ such that $AB=156$ and $AC=65$. We denote $H$ as the foot of the altitude from $A$. Determine the value of $AH$.

## 4 Junior Eliminatory: Solutions
Answer: 60. By Pythagoras, $B C=13 \times 13=169$, and the area of the right triangle is $\frac{1}{2} \times A B \times A C=\frac{1}{2} \times A H \times B C$.

## 6 Statements of the Animath Cup - June 2, 2015

Instructions

- Write the different problems on separate sheets. At the top left of each sheet, write in capital letters your last name and first name as well as your class, and the problem number at the top right.
- Complete solutions are required (except for exercise 1), where every statement is carefully justified. Grading will take into account the clarity and precision of the work.
- Work first in draft, and then write out your solution, or a well-written attempt at a solution containing significant results for the problem. Do not submit your drafts: they will not be considered.
- A complete solution will earn more points than several incomplete attempts. It is better to finish a small number of problems than to tackle all of them.
- Rulers, set squares, and compasses are allowed. Protractors are prohibited. Calculators are prohibited, as are all electronic devices.

Middle school students work on exercises 1 to 5. High school students work on exercises 4 to 8. Each exercise is graded out of 7 points.

Please respect the numbering of the exercises. Write the different problems on separate sheets. At the top left of each sheet, write in capital letters your last name and first name as well as your class, and the problem number at the top right.

## Middle School Statements