SolveMyMaths Action 6!

Creation of this resource was inspired by [url=https://twitter.com/solvemymaths/status/1058983944190918656]this tweet[/url] from [url=https://twitter.com/solvemymaths]Ed Southall[/url]. [br][br]The 2 circles are tangent to the square, the 2 diagonal segments, and each other.[br]The larger circle is also tangent to the right side of the square. [br][b][color=#9900ff][br]How can we formally prove what is dynamically illustrated here? [/color][/b]

Information: SolveMyMaths Action 6!