There are two circles, one with center A and radius 1, the other with center B and radius 2. The distance AB is 6. A third circle of unknown radius is tangent to both of these circles and there exists a straight line which
(1) is tangent to all three circles, and
(2) intersects the segment AB.
Find the radius of the third circle.
There are two solutions, R and r. Evaluate R - r.
+14913 There are two solutions, R and r. Evaluate R - r.
Hello Guest!
The distance \(\overline{AB}\) intersected by the tangent is divided into a and b.
\(a:(6-a)=r_A:r_B\\ a:(6-a)=1:2\\ 2a=6-a\\ a=2\\ b=4\)
\(r_A:(r_A+R)=a:\overline{AB}\\ 1:(1+R)=2:6\\ 6=2+2R \)
\(R=2\)
The radius of the third circle is 2.
There are not two solutions R.
!
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