Jubbly: "I''ve been seraching around the internet for a long time in search of an answer of how we use this theorem in life today?"

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Ceva's theoremis a well-known theorem in elementary geometry. Given a triangleABC, and pointsD,E, andFthat lie on linesBC,CA, andABrespectively, the theorem states that linesAD,BEandCFare concurrentif and only if

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the theorem pertains to elementary geometry, and its application is wide and many. theorem has also been generalized to triangles on other surfaces of constant curvature - Masal'tsev, L. A. (1994) "Incidence theorems in spaces of constant curvature."Journal of Mathematical Sciences, Vol. 72, No. 4

If you want it locally, it can be used in. . .land area measurement

- Grünbaum, Branko; Shephard, G. C. (1995),"Ceva, Menelaus and the Area Principle",Mathematics Magazine68(4): 254–268

Take a look at the familiar figure above, find the ratio of the pink triangle with the outside triangle if a,b, and c are 1/3 of lengrth of its side?

Ceva's theorem kills this off.

Yet, another proof without words of that line is even better.

ok

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