Problem A regular pentagon is inscribed in a circle with a diameter of $1 \ ft$.Find the length of one side of this regular pentagon. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution…

Problem There are two large circles and two small circles inside a rhombus as shown in the figure. If the longer diagonal of the rhombus is $85 \ inches$ and the shorter is $42 \ inches$, find the diameters of the large and small circles. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$…

Problem As shown in the figure, there is a circle and a rhombus inside a right-angled triangle. If the short side of the rectangular triangle is $15 \ inches$ and the long side is $36 \ inches$, find the diameter of the circle. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$…

Problem As shown in the figure, there are a large circle and two medium circles on a straight line, and there is a small circle inside the large circle. If the diameter of the large circle is $9 \ inches$ and the diameter of the middle circle is $6 \ inches$, find the diameter of…

Problem As shown in the figure, two large circles and two small circles are inscribed in a square, separated by oblique lines. If the diameter of the large circle is $1 \ inch$, what is the diameter of the small circle?   $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$…

Problem As shown in the figure, there are three equal circles inside the outer circle. If the diameter of the outer circle is $10 \ inches$, what is the diameter of the equal circle? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…

Problem As shown in the figure, in an outer circle with a diameter of $1 \ m$, there is a square, $4$ equal equilateral triangles, and $4$ equal circles. Then, find the diameter of the equal circle. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$…

Problem As shown in the figure, two equal circles touch each other on a straight line, and a square can be placed between them. If the diameter of the equal circle is $10 \ inches$, what is the length of one side of the square? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$…

Problem As shown in the figure, draw two diagonal lines inside an equilateral triangle and insert two equal circles. If the length of one side of the equilateral triangle is 10 inches, find the length of the diameter of the circle. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$…

Problem As shown in the figure, there are four circles inscribed in a right triangle, and there are large, medium, and small red circles between them. If the diameter of the large circle is $4$ inches and the diameter of the middle circle is $2$ inches, find the diameter of the small circle. $$ $$…