This geometry makes me happy | ITAMO 2000 - P2
Автор: Shefs of Problem Solving
Загружено: 2025-10-01
Просмотров: 367
Описание:
Problem Statement:
Let $ABCD$ be a convex quadrilateral, and write $\alpha=\angle DAB$, $\beta=\angle ADB$, $\gamma=\angle ACB$, $\delta= \angle DBC$ and $\epsilon=\angle DBA$. Assuming that $\alpha less than \pi/2$, $\beta+\gamma=\pi /2$, and $\delta+2\epsilon=\pi$, prove that $(DB+BC)^2=AD^2+AC^2$.
TIMESTAMPS:
00:00 Intro 20 - 30/60 - 150 Take 5/10
00:38 How to draw the diagram
02:00 The first question to ask yourself
02:25 Perspective shift + angle chase
03:30 The first idea
04:30 First approach
06:26 Reflecting on first idea
06:35 Second approach
08:25 The reason we do these simple ones first
09:45 The third solution using trig
12:40 Reflecting the trig solution
13:12 Reflecting on the problem and lesson on learning
15:00 Thanks for problem solving :)
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