Points $K$ and $M$ are taken on the sides $AB$ and $CD$ of square $ABCD$, respectively, and on the diagonal $AC$ - point $L$ such that $ML = KL$. Let $P$ be the intersection point of the segments $MK$ and $BD$. Find the angle $\angle KPL$.
Problem
Source: 2010 Oral Moscow Geometry Olympiad grades 8-9 p5
Tags: square, angles, equal segments
Quantum_fluctuations
16.08.2020 20:47
Does oral geometry olympiad means that one is not supposed to use any pen and paper? Also, what is the original source of problems from where you have taken all these problems?
parmenides51
16.08.2020 20:58
I think that oral means they have to present in person their solution to a judge and not give the handwritten solution this is my source
sunken rock
17.08.2020 23:26
Easy, $45^\circ$
Mikeglicker
17.08.2020 23:43
It is better if you can give a proper explanation rather then rating the problem's difficulty
AwesomeLife_Math
18.08.2020 00:19
Aren't there two possible values of the angle?
sunken rock
18.08.2020 12:41
Attached, self-explaining; if $K$ closer to $B$ than to $A$, then the answer is $135^\circ$. Best regards, sunken rock
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