Question

Fie ABC un triunghi isoscel AB=AC. Prin punctul M, M (apartine) BC, se duc paralele la AB si AC si se noteaza cu P si Q intersectiile lor cu dreptele AB respectiv AC. Sa se calculeze PM + QM stiind ca AB=10 cm.

Answer 1

Folosim teorema fundamantala a asemanarii:
[tex]PM||AC=> \frac{PM}{10} = \frac{BM}{BC}=>PM= \frac{10BM}{BC} \\ QM||AB=> \frac{QM}{10}= \frac{CM}{BC}=>QM= \frac{10CM}{BC} \\ PM+QM=\frac{10BM}{BC}+ \frac{10CM}{BC}= \frac{10(BM+CM)}{BC} = \frac{10BC}{BC} =10.[/tex]