18 segments

For discussing Olympiad level Geometry Problems
Joined:Thu Jun 23, 2016 1:55 pm
18 segments

Unread post by marek12 » Mon Jul 12, 2021 1:18 am

Adam has a circle of radius $1$ centered at the origin.

- First, he draws $6$ segments from the origin to the boundary of the circle, which splits the upper (positive $y$) semicircle into $7$ equal pieces.

- Next, starting from each point where a segment hit the circle, he draws an altitude to the $x$-axis.

- Finally, starting from each point where an altitude hit the $x$-axis, he draws a segment directly away from the bottommost point of the circle $(0,-1)$, stopping when he reaches the boundary of the circle.

What is the product of the lengths of all $18$ segments Adam drew?
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Ahnaf Sadik
Joined:Sun Sep 19, 2021 10:48 am

Re: 18 segments

Unread post by Ahnaf Sadik » Sun Sep 19, 2021 10:59 am

My head is spinning

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