Segment BF – isosceles triangle meridian AB (AB = BC). Point O lies on the side BC, the segment OP is the height of the triangle FOC. Are the lines BF and OP parallel?
By the condition of the problem, the segment BF is the median, and in an isosceles triangle there is also a bisector and a height. We are interested in the height, the BFC angle is 90 °.
In the FOC triangle, the segment OP is the conditional height, the OPC angle is 90 °.
Consider straight lines BF, OP and AC intersecting to them.
∠BFC = ∠OРС = 90 °.
These two angles are corresponding with straight lines BF, OP and secant AC and they are equal. We conclude that lines BF and OP are parallel.
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