|  |  | GEO0008 -- Orthocenter Theorem

## GEO0008 -- Orthocenter Theorem

##### The Theorem Statement [CGZ93]

Theorem. [Orthocenter Theorem] Given a triangle ABC, the three altitudes are concurrent in a point H.

##### The Image - GCLC 5.0

##### Prover's Code

    dim 100 100

    point A 10 10
    point B 50 10
    point C 40 70

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

    perp hA A a
    perp hB B b

    intersec H hA hB

    drawsegment A B
    drawsegment A C
    drawsegment B C

    drawline A H
    drawline B H

    cmark_lt A
    cmark_rt B
    cmark_lt C

    cmark_rt H

    drawdashline C H

    prove { equal { pythagoras_difference3 A C H  } { pythagoras_difference3 B C H } }

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

proofGEO0008.pdf

|  |  | GEO0008 -- Orthocenter Theorem