Best technique to solve this similar triangles problem?

Question:

Not sure how but I always get confused about going about how to solve it (I lost my working). After putting QX in form (1/6)PX and QX = (2/3)XR I'm abit confused on where to go from there, as I got 2/9 as an answer but its 4/9...

(edited 6 months ago)

Reply 1

tonyiptony

It's quite hard to have one trick to solve all geometry problems. Often times it comes down to (i) reading carefully what's given and what's the goal; then (ii) chasing the correct angles/sides, which takes a bit of intuition and luck.

In this particular problem, the fact that M is the midpoint of PR makes me want to find the length of PR... Well okay, we can't, but say QX is exactly 2 units long (why pick 2?), how long is other relevant (what do I mean by relevant?) lengths?

Kind of a silly question tbh.

(edited 6 months ago)