Question

Given a circle π(π; π = 4 ππ) and a line |π΄π΅| = 2 ππ. Determine and construct the set of all centers of circles that touch circle π and have radius π = |π΄π΅|

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Given a circle π with center π and radius π = 4 cm, and a line segment π΄π΅ 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 π and radius 4 cm - 2 cm = 2 cm. This is because the distance from π 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 π and radius 4 cm + 2 cm = 6 cm. This is because the distance from π 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 = 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 π as circle π.
Construction part: To construct these, you would draw two circles with the same center π, 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 = 2 cm.

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