Proving the Cyclic Quadrilaterals in Altitudes Problem | Geometry Help

[lolerlol]

Homework Statement

Let AD be and altitude of triangle ABC where angle A is 90 degrees.

Squares BCX1X2, CAY1Y2 and ABZ1Z2 are drawn outwards from the sides.

Let AX1 meet BY2 in U and AAX2 meet CZ1 in V

Prove that each of the quadrilaterals ABDU, ACDV and BX1UV is cyclic

Homework Equations

The Attempt at a Solution

I'm not sure where to start, but I've been given a clue

If angle BUA = angle BDA, the ABDU is cyclic
Let the point where BY2 meets AC be P
Consider triangles AUP and Y2CP

 

[Ouabache]

Welcome to physics forums! As you may have noticed, this is a great place to discuss ideas and problems you may encounter, in math and science.

On your problem, I would start by re-reading this https://www.physicsforums.com/showthread.php?t=94381. There are many knowledgeable people here, who are willing to steer you towards a successful solution. But first, you need to try to do some work on your problem and show us.

I recommend drawing the problem out as you've described it. A large drawing is useful, since you should see separation of the lines you draw, more clearly. I would also recommend using a pencil with a good eraser and a straight edge for this part.
Next, post what you have drawn as an image.

Can you tell us what a cyclic quadrilateral is?
(hint: if you cannot find it in your text, look it up on the web).