Question

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

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

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

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