Given the position and the radius of the violet and blue circles. I need to find the position of the pink circle which should touch all previous circles.
Any ideas?
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Represent the radius by an unknown, and apply the Pythagorean theorem. – quasi Apr 12 '18 at 10:24
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If you call the radii of the circles $R_a$, $R_b$ and $R_c$ and use the Pythagorean theorem one finds $$ (R_a + R_b)^2 + (R_a + R_c)^2 = (R_b + R_c)^2 $$ Solving for $R_c$ yields: $$ R_c = \frac{R_a(R_a+R_b)}{R_a-R_b}$$ If $R_a \neq R_b$. Filling in $R_a = 2$ and $R_b = 4$ (which I eyeballed from the picture) gives $R_c = 6$
Tim Dikland
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Since it has to touch all three blue circles (whose centers are aligned on the y-axis) and the problem is symmetric in the x-axis, the center of the purple circle should be on the x-axis. Hence the triangle is right-angled – Tim Dikland Apr 12 '18 at 11:59
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wow. so simple. I felt that I had to use the Pythagorean theorem, but couldn't understand how to represent hypotenuse and second cathetus. Thanks a lot! – Mezk Erei Apr 12 '18 at 12:21