MO circles

Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle with a center at point B passing through point A and a semicircle l with 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 touches the quarter circle k, semicircle l, and side AB. Find the radius of such a circle.

Correct answer:

r =  3 cm

Step-by-step explanation:

SO = SL + LO = R + 6  cm SB = BK   KS = 12 cm  r OE = OB  BE = 6 cm  r  SE² = SO²  OE² = SB²  BE² (6 + r)²  (6  r)² = (12  r)²  r² 12r + 12r = 144  24r 48r = 144 r=144/48=3 cm

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