Question

In a parallelogram ABCD, the line drawn through a point P on AB; parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R. Then, $\frac{AP}{PB}=$

• A. $\frac{AQ}{QC}$
• B. $\frac{AR}{RD}$
• C. $\frac{RQ}{QP}$
• D. $\frac{AC}{AP}$

Answer 1

Answer: (A), (B)

The correct options are
A

$\frac{AQ}{QC}$

B

$\frac{AR}{RD}$

In $\Delta ACD,$

QR || CD

$\frac{AQ}{QC}=\frac{AR}{RD}$ ..............(i)

In $\Delta ACB,$

PQ || CB

$\frac{AQ}{QC}=\frac{AP}{PB}$ ..............(i)

On comparing (i) & (ii), we get

$\frac{AP}{PB}=\frac{AR}{RD}$ ..............(iii)

Using result (i) & (ii) & (iii)

$\frac{AP}{PB}=\frac{AQ}{QC}=\frac{AR}{RD}$