Problem As shown in the figure, there is an equilateral triangle, one large circle, two medium circles, and one small circle within a square. If the diameter of the large circle is $9.5$ inches, find the diameter of the medium circle. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$…

Problem A circle is inscribed in an isosceles triangle with two equal sides of $10 \ inches$ and a base of $12 \ inches$.What is the diameter of the inscribed circle? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…

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. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$…