Question

In ∆ABC,the bisectors of angle B AC at D. A line PQ||AC meets,BC at P,Q and R respectively. Show that PRxBQ = QRxBP ​

Answer 1

Step-by-step explanation:

Given △ABC in which BD is the bisector of ∠B and a line PQ||AC meets AB,BC and BD at P,Q and R respectively.

Proof (i)

In △BQP, BR is the bisector of ∠B.

∴

BP

BQ

=

PR

QR

⇒ BQ.PR=BP.QR

⇒ PR.BQ=QR.BP [Hence proved]

(ii) In △ABC, we have

PQ∣∣AC [Given]

⇒

AP

AB

=

CQ

CB

[By Thale's Theorem]

⇒ AB×CQ=BC.AP [Hence proved]