Question about triangles

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

#Geometry #Proofs #Math

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Comments

Yes, it can be drawn!!!

Subhrodipto Basu Choudhury - 7 years, 11 months ago

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

Tim Vermeulen - 7 years, 11 months ago

what is median

PAYAL MANGLA - 7 years, 11 months ago

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

Piyal De - 7 years, 11 months ago

See this video.

Sri Kanth - 7 years, 11 months ago

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

Jan J. - 7 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.

Arshdeep Duggal - 7 years, 11 months ago

i think in Equilateral triangle median is angle bisector and altitude

A Former Brilliant Member - 7 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?

Budha Chaitanya - 7 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.

Michael Tong - 7 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.

Kiran Patel - 7 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.

David Kroell - 7 years, 11 months ago

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

David Kroell - 7 years, 11 months ago

it can be drawn

khaled ahmadi - 7 years, 11 months ago

yes

Hamsa Yousef - 7 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$