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MArishka [77]
2 years ago
11

An abstract painting is a square of side 96 cm, and shows three circles that touch each other and the sides of the square. The t

op two circles have the same radius. What is the radius of the third circle?

Mathematics
1 answer:
rodikova [14]2 years ago
6 0

Answer:

  27 cm

Step-by-step explanation:

The right triangle shown in the diagram can be used to find the radius r. By the Pythagorean theorem, ...

  24² + (72-r)² = (24+r)²

  576 + 5184 -144r +r² = 576 +48r +r²

  5184 = 192r

  5184/192 = r = 27 . . . . cm

The radius of the third circle is 27 cm.

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