In $\triangle\text{ABC},$ the bisector of $\angle\text{B}$ meets AC at D. A line PQ || AC meets AB, BC and BD at P, Q and R respectively.
Show that PR × BQ = QR × BP.
Show that PR × BQ = QR × BP.
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In triangle BQP, BR bisects angle B.
Applying angle bisector theorem, we get:
$\frac{\text{QR}}{\text{PR}}=\frac{\text{BQ}}{\text{BP}}$
⇒ BP × QR = BQ × PR
This completes the proof.
Applying angle bisector theorem, we get:
$\frac{\text{QR}}{\text{PR}}=\frac{\text{BQ}}{\text{BP}}$
⇒ BP × QR = BQ × PR
This completes the proof.
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