Two circles are given. which is the radius of a circle touching the data and having a center on a straight line passing through their centers, if the radii of these circles and the distance between their centers are respectively equal to 5, 2, 1.
A visual illustration of the location of the circles is given in the link.
Based on the fact that the radius of the first circle = 5 cm, and the radius of the second circle is 2 cm, the distance between the centers is 2 cm, then the second circle is inscribed in the second circle. Knowing that the third circle touches the first and second circles, it means that it is located to the right of the second circle or to the left of the second circle. If the third circle is located to the right of the second, then its radius is:
5-2-1 / 2 = 2/2 = 1 cm.
If the third circle is located to the left of the second, then its radius is:
5 + 1/2 = 6/2 = 3 cm.
Answer: 1 cm, 3 cm.
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