Question

In ΔPQR, X ∈ QR, such that Q-X-R. A line parallel to PR and passing through X intersects PQ in Y. A line parallel to PX and passing through Y intersects QR in Z. Prove that QZ/ZX=QX/XR.

Answer 1

Given: in ∆PQR, X ∈ QR, such that Q-X-R. A line parallel to PR and passing through X intersects PQ in Y. A line parallel to PX and passing through Y intersects QR in Z.

we have to prove : QZ/ZX = QX/XR

proof :- in ∆PQR, XY || PR ,
according to Thales theorem,
QY/YP = QX/XR ........(i)

in ∆PQX, YZ || PX ,
according to Thales theorem,
QY/YP = QZ/ZX ........(ii)

from eqs. (i) and (ii),
QX/XR = QZ/ZX
hence proved