Woman's day

We can easily make a heart for mothers for Woman's day by drawing two semicircles on the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1?

Final Answer:

r =  0.65

Step-by-step explanation:

$$\begin{gathered} a=1 \\ {r}_1=a/4=1/4=\frac{1}{4}=0.25 \\ {r}^2=r_1^2+(a-r+r_1{)}^2 \\ {r}^2=r_1^2+(a-r+r_1{)}^2 \\ {r}^2=0.25^2+(1-r+0.25{)}^2 \\ 2.5r=1.625 \\ r=\frac{1.625}{2.5}=0.65 \\ r=\frac{13}{20}=0.65 \end{gathered}$$

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