Diameters AB and CB are drawn in a circle with center O. AB = 20 cm. AC = 6 cm. Find the perimeter of the triangle BOD.

Since AB and CD are the diameters of a circle centered at point O, this point is the point of their intersection and divides the diameters in half: AO = OB, CO = OD = 20 cm / 2 = 10 cm.
This means that the perimeter of the AOC triangle is 2 * 10 cm + 6 cm = 26 cm.
The triangles Δ AOC and Δ BOD are isosceles, with ∠AOC = ∠BOD (vertical angles are equal).
According to the “First sign of triangle equality”, triangles AOC and BOD are equal. Therefore, the perimeter Δ BOD is also 26 cm.
Answer: 26 cm.