In the given figure, PQ | BA and PR | CA. If PD = 12 cm, find BD x CD.
Answers
Answer:
where is the figure of the question
Answer:
bd * cd = 144
Step-by-step explanation:
1234
Q. 14.4( 7 Votes )
In the given figure PQ is parallel to BA and PR is parallel to CA. If PD = 12cm. Find BD × CD.

Answer
Given: PQ || BA, PR || CA, PD = 12 cm
To find: BD × CD
Concept Used: Basic Proportionality Theorem
Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
In ∆ BRD, PQ || BR as PQ || BA
So by basic Proportionality Theorem,
……(i)
In ∆ PRD, CQ || PR as PR || CA
So By basic proportionality theorem.
……(ii)
From eq (i) and eq (ii)

Cross multiplying we get,
PD × PD = BD × CD
⇒ BD × CD = PD2 = 122
⇒ BD × CD = 144
∴ the product of BD and CD is 144.
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