Pick any point M on AC. Draw a circle centered at M with radius AM. Pick point N on BC so BN=AM. Through N draw a parallel to AB; it will intersect the circle at N'. Through N' draw a parallel to BC; it will intersect AB at B' and AC at C'.
Now, triangle AB'C' is similar to ABC, and M and N' are such that AM=MN'=N'B'. Scale AB'C' up so AB' becomes AB (and AC' becomes AC) and then M will become P and N' will become Q.
(Note that scaling the triangle can be done with compass and straightedge; it's a classical construction.)
Comments: (
You must be logged in to post comments.)
