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Problem 195

Geometry Difficulty 1.3 Multiple choice CEMC Gauss (Grade 7) · Canada · 2023

A circle has a radius of 4 cm. A line segment joins two points on
the circle. What is the greatest possible length of the line
segment?

Pick one

Official solution

The line segment with greatest length that joins two points on a
circle is a diameter of the circle. Since the circle has a radius of 4
cm, then its diameter has length $2\times4 \text{ cm}=8$ cm, and so the greatest possible length of the
line segment is 8 cm.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.