Problem As shown in the figure, an oblique line $AB$ has been drawn on the fan, and the greater and smaller circles are inscribed on either side of $AB$. When the diameter of the greater circle, and the lengths of $OD$ and $AD$ are known, find the diameter of the small circle and the length…

Problem As shown in the figure, there are two circles, a larger and a smaller, inside a right triangle, which touch each side. The two circles are in contact across the oblique line $AD$ drawn from the point $A$ to the side $BC$. When you know $BD$, $∠ABD$, and $∠ADC$, find the diameters of the…

Problem As shown in the figure, two regular pentagons, one large and one small, are placed on a line, adjacent to each other.When you know the area of ​​an isosceles triangle in which base is one side of the larger regular pentagon and the angle of its vertex, find the lengths of the sides of…