MO circles

Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a circle that would lie inside the square and touch the quarter circle k, semicircle l and side AB. Find the radius of such circle.

Correct result:

r =  3 cm


SO=SL+LO=R+6 SB=BKKS=12r OE=OBBE=6r  SE²=SO²OE²=SB²BE² (6+r)²(6r)²=(12r)²r² 12r+12r=14424r 48r=144 r=144/48=3 cm

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