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OlympiadBench / 1828 / There are 2017 mutually external circles drawn on a blackboard, such that no two…

Problem

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question

There are 2017 mutually external circles drawn on a blackboard, such that no two are tangent and no three share a common tangent. A tangent segment is a line segment that is a common tangent to two circles, starting at one tangent point and ending at the other one. Luciano is drawing tangent segments on the blackboard, one at a time, so that no tangent segment intersects any other circles or previously drawn tangent segments. Luciano keeps drawing tangent segments until no more can be drawn. Find all possible numbers of tangent segments when he stops drawing.

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1828
task_id: a2be9cc2-73e4-517d-81f6-50985bf2f4b0
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1828
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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