The length of a line segment AB is 2 cm It is divided into two parts at a point C such that AC2 AB t...........

Quantitative Aptitude (CDS) Mensuration 2D

The length of a line segment AB is 2 cm. It is divided into two parts at a point C such that AC2 = AB × CB. What is the length of CB?

$3\sqrt{5}\: cm$

$3-\sqrt{5}\: cm$

$5\sqrt{3}\: cm$

$\sqrt{5} -1\: cm$

AB line segment is divided into two parts at point C, let AC = x , BC = 2 - x As per equation given in the statement (AC² = AB * CB)

x² = 2 * (2-x)

x² = 4-2x

x² +2x - 4 = 0 on solving this equation; x = -1 + √5

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