This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 4

2020 Novosibirsk Oral Olympiad in Geometry, 1
Tags: geometry , rectangle , tangent circles , semicircles
Two semicircles touch the side of the rectangle, each other and the segment drawn in it as in the figure. What part of the whole rectangle is filled? [img]https://cdn.artofproblemsolving.com/attachments/3/e/70ca8b80240a282553294a58cb3ed807d016be.png[/img]

Durer Math Competition CD 1st Round - geometry, 2014.C2
Tags: geometry , semicircles , equal segments , Durer
Above the segments $AB$ and $BC$ we drew a semicircle at each. $F_1$ bisects $AB$ and $F_2$ bisects $BC$. Above the segments $AF_2$ and $F_1C$ we also drew a semicircle at each. Segments $P Q$ and $RS$ touch the corresponding semicircles as shown in the figure. Prove that $P Q \parallel RS$ and $|P Q| = 2 \cdot |RS|$. [img]https://cdn.artofproblemsolving.com/attachments/8/2/570e923b91e9e630e3880a014cc6df4dc33aa2.png[/img]

2013 BMT Spring, 2
Tags: semicircle , semicircles , geometry
S-Corporation designs its logo by linking together $4$ semicircles along the diameter of a unit circle. Find the perimeter of the shaded portion of the logo. [img]https://cdn.artofproblemsolving.com/attachments/8/6/f0eabd46f5f3a5806d49012b2f871a453b9e7f.png[/img]

Novosibirsk Oral Geo Oly IX, 2020.1
Tags: geometry , rectangle , tangent circles , semicircles
Two semicircles touch the side of the rectangle, each other and the segment drawn in it as in the figure. What part of the whole rectangle is filled? [img]https://cdn.artofproblemsolving.com/attachments/3/e/70ca8b80240a282553294a58cb3ed807d016be.png[/img]