Question

In the given fig PQ||BA, PR||CA. If PD=12cm. Find BD*CD

Answer 1

In triangle DPR. CQ parallel PR
Therefore. DC \CP= DQ \QR.............1
Similarly in triangle dbr.
DP\ PB=DQ\QR.,..............2
From 1&2
DC\CP=DP\PB
DC.PB=CP.DP
DC(BD-PD) = (PD-CD) DP
DC.BD-12CD=144-12CD
Therefore BD.CD =144

Answer 2

$BD \times CD = 144 cm$

Step-by-step explanation:

Given:

PQ║BA and PR║CA

So, PQ║BA

⇒ PQ║BR

Now, In Δ BDR

PQ║BR

By Basic Proportionality Theorem, we get

$\frac{PD}{BD} =\frac{DQ}{DR}$                    [1]

PR║CA                                                        [Given]

⇒ PR║CQ

Now,In Δ PRD

PR║CQ

By Basic Proportionality Theorem, we get

$\frac{CD}{PD}= \frac{DQ}{DR}$                     [2]

From (1) and (2) , we get

$\frac{PD}{BD} =\frac{CD}{PD}$

⇒ $BD \times CD = (12)^2$

⇒ $BD \times CD = 144 cm$

Hence $BD \times CD = 144 cm$.