pow:start
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pow:start [2024/04/09 13:51] mazur |
pow:start [2024/05/07 15:59] (current) mazur |
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| ====== Problem of the Week ====== | ====== Problem of the Week ====== | ||
| ~~NOTOC~~ | ~~NOTOC~~ | ||
| - | <box 85% round orange|Problem 6 (due Monday, April 22) > | + | <box 85% round orange| > |
| - | Let $ABCD$ be a convex quadrilateral whose diagonals $AC$ and $BD$ intersect at | + | The problem of the week will return in the Fall 2024 semester. We thank everyone who participated this Spring. For the Summer, we suggest reviewing problems from past semesters and working on the additional problems posted at the bottom of the provided solutions. |
| - | a point P. Let $M,N$ be the midpoints of the sides $AB$ and $CD$ respectively. | + | |
| - | Prove that the area of the triangle $PMN$ is equal to the quarter of the absolute value of the difference | + | |
| - | between the area of the triangle $DAP$ and the area of the triangle $BCP$: | + | |
| - | \[ \text{area}(\triangle MNP)=\frac{1}{4}\left|\text{area}(\triangle DAP)-\text{area}(\triangle BCP)\right |.\] | + | |
| </box> | </box> | ||
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| ===== Previous Problems and Solutions===== | ===== Previous Problems and Solutions===== | ||
| + | |||
| + | * [[pow:Problem7s24|Problem 7]] Solved by Sasha Aksenchuk. | ||
| + | |||
| + | * [[pow:Problem6s24|Problem 6]] Solved by Sasha Aksenchuk. | ||
| * [[pow:Problem5s24|Problem 5]] We did not receive any solutions. | * [[pow:Problem5s24|Problem 5]] We did not receive any solutions. | ||
pow/start.1712685097.txt · Last modified: 2024/04/09 13:51 by mazur