__A simple geometrical theorem I did not know__

Given:

AE = α•AC

ED = β•EB

FD = γ•FC

Denoting with (PQR) the area of ΔPQR, we observe

(ADB) = γ•(ACB) and also

(ABD) = (1–β)•(AEB)

= (1–β)•α•(ACB)

from which we conclude γ = (1–β)•α .

[ The theorem we used thrice—say (PQR)•RS/QR = (PRS)—is no more than adding metric to —see EWD1221b—

*R ≠ S*∧ col.R.S.Q ∧ tri.R.Q.P ⇒ tri.R.S.P ]

The theorem proved in this note is of no importance; it is recorded here because I don't remember this proof technique from my school-days.

transcribed by Swarup Sahoo

last revisedSun, 26 Jun 2011

Nuenen, 22 December 1995

prof. dr. Edsger W. Dijkstra

Department of Computer Sciences

The University of Texas at Austin

Austin, TX 78712-1188

transcribed by Swarup Sahoo

last revised