10. Four circles of radius $5 \mathrm{~cm}$ touch the sides of a square and each other, as shown in the diagram. On each side of the square, an equilateral triangle is drawn to form a four-pointed star.
What is the perimeter of the star?
A $40 \mathrm{~cm}$
B $80 \mathrm{~cm}$
C $120 \mathrm{~cm}$
D $160 \mathrm{~cm}$
E $200 \mathrm{~cm}$
10. D The radius of each of the circles is $5 \mathrm{~cm}$ and hence the diameter of each is $10 \mathrm{~cm}$. The length of the side of the square is equal to the sum of the diameters of two circles and hence is equal to $20 \mathrm{~cm}$. The length of each side of the equilateral triangle is equal to the length of the side of the square. Hence the perimeter of the star, which is made up of eight sides of congruent equilateral triangles, is $8 \times 20 \mathrm{~cm}=160 \mathrm{~cm}$.