In triangle ABC, O is the point of intersection of the middle perpendiculars. AO = 10 cm.

In triangle ABC, O is the point of intersection of the middle perpendiculars. AO = 10 cm. Find the perimeter of the triangle BOC if BC = 12 cm.

By the property of the median perpendiculars of the triangle, the point O, the intersection of the median perpendiculars is the center of the circle circumscribed around the triangle. Then ОА = ОВ = ОС and are the radii of the circle. Since, by condition, AO = 10 cm, then OS = OB = 10 cm.

Determine the perimeter of the BOС triangle.

Pvos = ВO + CO + BC = 10 + 10 + 12 = 34 cm.

Answer: The perimeter of the ВOС triangle is 34 cm.