Problem As shown in the figure, two diagonal lines are drawn inside the trapezoid such that $∠B = ∠C = ∠R$. Two congruent circles are inscribed so that each one is tangent to the diagonal lines and to the sides of the trapezoid. If the length of the base $BC$ is $12 \ inches$ and…

Problem As shown in the figure, inside the right triangle $ABC$ (with $∠B = ∠R$), there is another right triangle that shares the shorter side $AB$. In addition, two congruent circles are placed on the left and right sides of triangle $ABC$, each tangent to the two line segments drawn from vertices $A$ and $B$…

Problem As shown in the figure, the upper and lower congruent circles are mutually tangent, and the lower circle is tangent to a line.The left and right congruent circles are each tangent to both the upper and lower circles.A small circle is tangent to the two congruent circles and also tangent to a line.If the…

Problem As shown in the figure, two congruent circles are inscribed in an isosceles trapezoid. If the upper base of the trapezoid is $2.4 \ inches$ and the lower base is $12 \ inches$, find the diameters of the circles. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$…

Problem As shown in the figure, two squares—one large and one small—each contain an inscribed circle. If the diameters of the larger and smaller circles are $18 \ inches$ and $8 \ inches$, respectively, find the length of one side of the larger square. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$…

Tsukama Shrine is located 2 kilometers southeast of JR Matsumoto Station.   Problem As shown in the figure, a great circle circumscribes an isosceles triangle. The great circle also contains two congruent circles, each tangent to the sides of the isosceles triangle. Inside the isosceles triangle, there is another congruent circle inscribed. If the diameter…