A straight line parallel to BC of ∆ABC intersects

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A straight line parallel to BC of ∆ABC intersects AB and AC at points P and Q respectively. AP = QC, PB= 4 units and AQ = 9 units, then the length of AP is :

1. 25 units
2. 3 units
3. 6 units
4. 6.5 units

Correct Option: C

On the basis of question we draw a figure of a ∆ABC in which a straight line parallel to BC intersects AB and AC at points P and Q respectively.

Given , AP = QC, PB= 4 units and AQ = 9 units
PQ || BC

∴	AP	=	AQ
	AB		AC

[By Basic Proportionality Theorem ]

⇒	AB	=	AC
	AP		AQ

⇒	AP + PB	=	AQ + QC
	AP		AQ

⇒	PB	=	QC	=	AP
	AP		AQ		AQ

⇒ AP² = PB. AQ = 4 × 9 = 36
∴ AP = 6 units