B1 is a point on the side AC of ∆ABC and B1B is joined.

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B₁ is a point on the side AC of ∆ABC and B₁B is joined. A line is drawn through A parallel to B₁B meeting BC at A₁ and another line is drawn through C parallel to B₁B meeting AB produced at C₁. Then

According to question , we draw a figure

In ∆ AA₁C and ∆BB₁C,
BB₁ || AA₁ ⇒ ∆AA₁C ~ ∆BB₁C

∴	AA₁	=	AC	..... (i)
	BB₁		B₁C

In ∆ ACC₁ and ∆ ABB₁,
BB₁ || CC₁ ⇒ ∆ACC₁ ~ ∆ABB₁

∴	CC₁	=	AC
	BB₁		AB₁

⇒	BB₁	=	AB₁	=	AC - B₁C
	CC₁		AC		AC

⇒	BB₁	= 1 -	B₁C
	CC₁		AC

⇒	BB₁	= 1 -	BB₁	[From equation (i)
	CC₁		AA₁

⇒	BB₁	+	BB₁	= 1
	CC₁		AA₁

⇒	1	+	1	=	1
	CC₁		AA₁		BB₁