B1 is a point on the side AC of ΔABC and B1B is joined. 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:
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Correct answer: B
Explanation
The correct answer is Option 2 i.e.
In ΔAA1C and ΔBB1C:
BB1 || AA1
BB1/AA1 = B1C/AC --- (1)
In ΔCC1A and ΔABB1:
BB1 || CC1
BB1/CC1 = AB1/AC
⇒ BB1/CC1 = (AC – B1C)/AC
⇒ BB1/CC1 = 1 – (B1C/AC)
From equation (1):
BB1/CC1 = 1 – BB1/AA1
⇒ BB1[1/CC1 + 1/AA1] = 1
⇒ 1/CC1 + 1/AA1 = 1/BB1