Another brick

A rectangle and a quarter circle. What is the area of the rectangle?

Scroll down for a solution to this problem.


The rectangle area is 168.

Solution by Bannu.

First notice the 3-4-5 triangle AFC. It gives us the rectangle diagonal: x2+y2=252.

Next we discern the cyclic quadrilateral AFDC. It has known diagonals and two known sides. The unknown sides are exactly the rectangle sides we need. Now we can use Ptolemy’s Theorem. It gives 15x+20y=20*25.

Solving these two equations gives x=24 and y=7, leading to an area of 168.

🤞 Don’t miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.

Leave a Reply

Your email address will not be published. Required fields are marked *

Optionally add an image (JPEG only)