If three one rupee coins can be placed around a ten-paise coin such that each one rupee coin touches the ten paise coin as well as the other two one-rupee coins, the ratio of the radii of the one rupee and ten paise coin is :

If three one rupee coins can be placed around a ten-paise coin such th

1.	If three one rupee coins can be placed around a ten-paise coin such that each one rupee coin touches the ten paise coin as well as the other two one-rupee coins, the ratio of the radii of the one rupee and ten paise coin is :
Answer» Let `R` is the radius of 1-rupee coin and `r` is the radius of 10 paise coin. We can create a diagram with the given details. If we join centers of all 1-rupees coin, it will form an equilateral triangle `ABC`. Please refer to video for the diagram. If `O` is the center of 10 paise coin, then, `/_OAB = /_OBA = 60/2 = 30^@` Here, `AB = 2R and OA = r+R`. So, we can say that, `2(r+R)cos30^@ = 2R` `(r+R)/R = 2/sqrt3` `r/R + 1= 2/sqrt3=> r/R = 2/sqrt3-1` `r/R = (2-sqrt3)/sqrt3 = (2sqrt3-3)/sqrt3`, which is the required ratio.