Can a triangle be formed by the three special cevians of a triangle, altitude,median,angle bisector...?

Note by Kishan K
4 years, 11 months ago

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I suppose you mean the altitude, median and bisector of just one angle? As opposed to one cevian from each angle.

- 4 years, 11 months ago

Yes, it can be drawn!!!

- 4 years, 11 months ago

yes

- 4 years ago

it can be drawn

- 4 years, 11 months ago

Simple Sin or Cosin rule can be used to determine those lengths.

- 4 years, 11 months ago

Is your question asking if three of the same type of cevian (e.g. 3 medians) form a triangle, i.e. be non-concurrent, or if three of any type of cevian? If the latter then yes. I'm not sure about the former yet.

- 4 years, 11 months ago

I think he is trying to ask that if we draw an altitude from A , a median from B ,and an angle bisector of C.Then will they form a triangle.?Correct me if i am wrong.Obviously it will not form in equilateral triangle.

- 4 years, 11 months ago

Well yes it would be possible in both cases. If we knew the lengths and the angles. even if it was equilateral. simple Sine and Cosine rules can be used to determine those lines that thus make the triangle.

- 4 years, 11 months ago

yes, in equilateral triangle it is possible i think.As median itself makes angle bisector and also the altitude. Am i right?

- 4 years, 11 months ago

i think in Equilateral triangle median is angle bisector and altitude

- 4 years, 11 months ago

Yes indeed. You can get expressions of the lengths of sides if the 3 medians or bisectors are given. Solve them. Then you know the length of each side.

- 4 years, 11 months ago

what is median

- 4 years, 11 months ago

See this video.

- 4 years, 11 months ago

A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side.

- 4 years, 11 months ago

I'm kinda surprised that you know what is cevian and not median. ;O

- 4 years, 11 months ago