Question

In ∆ABC, the bisector of ∠B meets AC at D. A line OQ║AC meets AB, BC and BD at O, Q and R respectively. Show that BP × QR = BQ × PR

Answer 1

In triangle BQO, BR bisects angle B. 

Applying angle bisector theorem, we get: 

QR/PR = BQ/BP 

⇒ BP × QR = BQ × PR 

This completes the proof