Stengel's Theorem

E

0.66

D

0.53

G

0.6

EI

≈

8.889

DH

≈

7.138

FJ

≈

5.607

BG

≈

13.469

1

EI

+

1

DH

≈

0.253

1

FJ

+

1

BG

≈

0.253

Let ABC be a triangle. Let E, D, and G be points on AB, BC, and AC, respectively. Let EC intersect AD at F. Choose points I, J, and H so that EI || BG || FJ || DH.

Then

1

EI

+

1

DH

=

1

FJ

+

1

BG

.

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