Euclid's Second Proposition in the Poincaré disk

Feel free to move points A, B, and C. Euclid's Second Proposition in the Poincaré disk To place a straight line equal to a given straight line with one end at a given point. Let A be the given point, and BC the given straight line. It is required to place a straight line equal to the given straight line BC with one end at the point A. Join the straight line AB from the point A to the point B, and construct the equilateral triangle DAB on it. Produce the straight lines AE and BF in a straight line with DA and DB. Describe the circle CGH with center B and radius BC, and again, describe the circle GKL with center D and radius DG.