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# help

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As shown in the figure, circle of diameter 4 touches the other two circles and the bottom of the rectangle. Circle of diameter 3 touches the top at A and left side of the rectangle. Circle of diameter 6 touches the top at B and two other sides of the rectangle. Find the length of AB.

Dec 2, 2019

#1
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As shown in the figure, circle of diameter 4 touches the other two circles and the bottom of the rectangle.

Circle of diameter 3 touches the top at A and left side of the rectangle.

Circle of diameter 6 touches the top at B and two other sides of the rectangle.

Find the length of AB.

$$AB = x+y$$

$$\begin{array}{|rcll|} \hline (1.5+2)^2 &=& x^2+(6-1.5-2)^2 \\ 3.5^2 &=& x^2+2.5^2 \\ x^2 &=& 3.5^2-2.5^2 \\ x^2 &=& 6 \\ x &=& \sqrt{6} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline (2+3)^2 &=& y^2 + (3-2)^2 \\ 5^2 &=& y^2 +1 \\ y^2 &=& 25-1\\ y^2 &=& 24 \\ y^2 &=& 4*6 \\ y &=& 2\sqrt{6} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline AB &=& x+y \\ AB &=& \sqrt{6}+2\sqrt{6} \\ \mathbf{AB} &=& \mathbf{3\sqrt{6}} \\ \hline \end{array}$$

Dec 3, 2019