Point F lies on side AC of triangle ABC so that BF = FC, point O is the midpoint of side BC. Which segment FO or FC is greater and why?
FO is the median (BO = OC) in the isosceles triangle BFC, drawn to the base, hence FO is also the height. Therefore, triangle FOC is rectangular with hypotenuse FC and legs FO and OC. The hypotenuse is always larger than the legs.
Answer: FC> FO.
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