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In $Δ A B C, \bar{P Q} ∥ \bar{A B}$ and $P, Q$ are on $B C$ and $C A$ respectively. If $C Q : Q A = 1 : 3$ and $C P = 4,$ then $B C =$

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detailed solution

Correct option is C

From figure

$Δ A B C, \bar{P Q} ∥ \bar{A B}$

$\frac{C P}{C B} = \frac{C Q}{C A}$ (by BPT)

$\Rightarrow \frac{4}{C B} = \frac{1}{4}$

$\Rightarrow B C = 4 \times 4 = 16$

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In ΔABC,PQ¯∥AB¯ and P,Q are on BC and CA respectively. If CQ:QA=1:3 and CP=4, then BC=