A square of variable size inscribed in a semicircle of radius r. What is the maximum distance d of the lowest square vertex to the nearest semicircle corner?

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## Solution

The maximum d is (2-√2)r.

geometry puzzles

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- Post author By Rik D. Tangerman
- Post date March 11, 2022
- 2 Comments on The sliding square

A square of variable size inscribed in a semicircle of radius r. What is the maximum distance d of the lowest square vertex to the nearest semicircle corner?

Scroll down for a solution to this problem.

The maximum d is (2-√2)r.

## 2 replies on “The sliding square”

I like your website.

The proof of “The sliding square” seems for me not complete:

The assumption that the angle at the midpoint of the circle opposite to the chord a is 2*theta ist not valid for every “sliding square”. So there is a gap in the proof.

Here are the corners of one of these sliding squares:

A(6-4*sqrt(6)|-8+4*sqrt(6))

B(14-4*sqrt(6)|0)

C(6|8)

D(-2|4*sqrt(6))

with C, D on the circle with center O(0|0) and radius 10.

Peter

Thank you Peter. You are right. I opted for another solution.