|  |  | GEO0001 -- Ceva's Theorem

## GEO0001 -- Ceva's Theorem

##### The Theorem Statement [CGZ93]

Theorem. [Ceva's Theorem] Let DeltaABC be a triangle and P be any point in the plane. Let D=AP cap CB, E=BP cap AC, and F=CP cap AB. Show that: (AF)/(FB) × (BD)/(DC) × (CE)/(EA) = 1 P should not be in the lines parallels to AC, AB and BC and passing through B, C and A respectively.

##### The Image - GCLC 5.0

##### Prover's Code

    point A 60 10
    point B 30 90
    point C 80 90
    point P 55 75

    line a B C
    line b A C
    line c A B

    line pa P A
    line pb P B
    line pc P C

    intersec D a pa
    intersec E b pb
    intersec F c pc

    drawsegment A B
    drawsegment A C
    drawsegment B C

    drawsegment A D
    drawsegment B E
    drawsegment C F

    cmark_b A
    cmark_t B
    cmark_t C
    cmark_t D
    cmark_lt F
    cmark_rt E
    cmark_t P

    prove { equal { mult { mult { sratio A F F B } { sratio B D D C } } { sratio C E E A } } 1 }

##### Proved -- Proof, made with GCLC, v1.0

proofGEO0001.pdf

|  |  | GEO0001 -- Ceva's Theorem