Three circles fit inside a square as shown where two small circles touch a large circle. Given that the radius of the small circles is 3 and the side length of the square is 14, find the radius of the larger circle
+128474 Let the center of the large circle be = (7,R)
Then the center of one of the small circles is (11, 11)
So the square of the distance between these two points is (R + 3)^2
So
(7-11)^2 + (11 - R)^2 = (R + 3)^2
4^2 + R^2 - 22R + 121 = R^2 + 6R + 9 simplify
137 - 22R = 6R + 9
137 - 9 = 28R
128 = 28R
128/28 = R = 32/7
+1639 Three circles fit inside a square as shown where two small circles touch a large circle. Given that the radius of the small circles is 3 and the side length of the square is 14, find the radius of the larger circle
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Square side = 14 small radius r = 3 big radius R = ?
The distance between the centers of the small circles is 8 units.
So, we have 42 + (11 - R)2 = (3 + R)2 R = 32 / 7 or R ≈ 4.57
