Question

Given a circle ๐‘˜(๐‘†; ๐‘Ÿ = 4 ๐‘๐‘š) and a line |๐ด๐ต| = 2 ๐‘๐‘š. Determine and construct the set of all centers of circles that touch circle ๐‘˜ and have radius ๐‘Ÿ = |๐ด๐ต|

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Answer to a math question Given a circle ๐‘˜(๐‘†; ๐‘Ÿ = 4 ๐‘๐‘š) and a line |๐ด๐ต| = 2 ๐‘๐‘š. Determine and construct the set of all centers of circles that touch circle ๐‘˜ and have radius ๐‘Ÿ = |๐ด๐ต|

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Tiffany
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Given a circle ๐‘˜ with center ๐‘† and radius ๐‘Ÿ = 4 cm, and a line segment ๐ด๐ต with length 2 cm. The circles that touch circle ๐‘˜ and have radius 2 cm will either be inside or outside of circle ๐‘˜. For the circles inside ๐‘˜, their centers will lie on a circle with the same center ๐‘† and radius 4 cm - 2 cm = 2 cm. This is because the distance from ๐‘† to the center of the smaller circle is the difference of the radii. For the circles outside ๐‘˜, their centers will lie on a circle with the same center ๐‘† and radius 4 cm + 2 cm = 6 cm. This is because the distance from ๐‘† to the center of the larger circle is the sum of the radii. So, the set of all centers of circles that touch circle ๐‘˜ and have radius ๐‘Ÿ = 2 cm will lie on two circles, one inside ๐‘˜ with radius 2 cm and one outside ๐‘˜ with radius 6 cm, both having the same center ๐‘† as circle ๐‘˜. Construction part: To construct these, you would draw two circles with the same center ๐‘†, one with radius 2 cm and the other with radius 6 cm. The points on these two circles represent the centers of all possible circles that touch circle ๐‘˜ and have radius ๐‘Ÿ = 2 cm.

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