Question

Anoop managed to draw 6 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the r atio of the side of the square to the radius of the circles. Assume √2 is 1.4.

Answer 1

Answer:

Step-by-step explanation:

Draw tangents to circle and join them to centre

Now j

Answer 2

Answer:

Ratio of the square to the Radius of the circle is 1:(2 + 6√2)

Step-by-step explanation:

Step 1:

Let us assume  

r be the radius of a circle  

d  be the diagonal of square  

s be the side of square  

Step 2:

The distance from the center of an extreme circle to the nearest corner is r√2  

d = 12r + 2×r√2  

= 2r(6+√2)  

Step 3:

Use the Pythagorean theorem to find s:  

$\begin{array}{l}{\mathrm{s}^{2}+\mathrm{s}^{2}=\mathrm{d}^{2}} \\ {2 \mathrm{s}^{2}=(2 \mathrm{r}(6+\sqrt{2}))^{2}} \\ {2 \mathrm{s}^{2}=4 \mathrm{r}^{2}(6+\sqrt{2})^{2}} \\ {\mathrm{s}^{2}=2 \mathrm{r}^{2}(6+\sqrt{2})^{2}} \\ {\left.\mathrm{s}=\sqrt{( } 2 \mathrm{r}^{2}(6+\sqrt{2})^{2}\right)}\end{array}$

s = r(6+√2)√2  

s = r(2 + 6√2)  

Step 4:

r:s = 1:(2 + 6√2)