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. $$ $$…

Problem As shown in the figure, if there is a round field with a diameter of $100 \ m$ and it is divided equally among $5$ people, find the length of each of the red and blue line segments. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$…

Problem As shown in the figure below, two equilateral triangles $ACE$ and $BDF$ are inscribed in a regular hexagon $ABCDEF$, and a great circle with a diameter of $1 \ m$ is inscribed in them. If a small circle with a diameter of $t \ m$ is inscribed in an isosceles triangle $ABF$, and small…

Problem There is a right triangular piece of land with a short side of $30\ m$ and a long side of $40 \ m$. As shown in the diagram, add $2 \ m$ wide roads to this, and divide the remaining area equally into three sections, $S_1, S_2$, and $S_3$. What are their shapes? And…

Katayama-hiko Shrine is located $850$ meters southeast from Osafune Station on the JR Ako Line. Problem As shown in the figure, two mutually circumscribed circles of diameter $d$ are inscribed in a fan of radius $R$. $c$ is the common tangent of these two circles, and is also the chord of the fan that inscribes…