Own work. Geometry is partially based on the flag description found in the constitution of Timor-Leste. The relevant constitutional text can be found (in Portuguese) at Símbolos Nacionais.

The national flag is rectangular and formed by two isosceles triangles with overlapping bases, with a black triangle with a height equal to one third of the length that overlaps the yellow one, whose height is half the length of the flag. In the center of the black triangle is placed a five-pointed white star, which symbolizes the guiding light. The white star has one of the points facing the upper left edge of the flag. The remaining part of the flag is colored red.

— Google translation of Portuguese text found at Símbolos Nacionais

The aspect ratio of the flag and the size of the star are not defined by the constitution. Also, the constitution does not adequately define the location of the star because the centre of the black triangle can mean either its Geometric Center (Centroid) or its Incenter.

For the purposes of this construction sheet three assumptions are made:

1. The aspect ratio of the flag is assumed to be 1:2. See UNTAET note below.
2. The diameter of the imaginary circle around the star is assumed to be ¹⁄₃ the width of the flag (or ¹⁄₆ the length of the flag).
3. The centorid of the star and the centroid of the black triangle share a common point. i.e. the star and the imaginary circle around the star are both centered on the centroid of the triangle.

The same assumptions are reflected in the construction sheet shown at Vexilla-Mundi. The same (or very similar) assumptions also appear to have been used when creating the primary GIF image of the flag shown at Flags of the World (FOTW).