GATE (GA) Textile 2020 Question Paper Solution | GATE/2020/GA/09

Question 09 (General Aptitude)

Q.9	Given a semicircle with O as the centre, as shown in the figure, the ratio $\frac{\overline{AC}+\overline{CB}}{\overline{AB}}$ is _________, where $\overline{AC}$ , $\overline{CB}$ and $\overline{AB}$ are chords.
(A)	$\sqrt{2}$
(B)	$\sqrt{3}$
(C)	2
(D)	3

gate 2020 textile question no 9

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AB is the diameter of semicircle i.e. Let, AB=2a and radius AO=CO=OB=a

AC and CB are the chords

$AC=CB=a\sqrt 2$

Then,

$\frac{\overline{AC}+\overline{CB}}{\overline{AB}}=\frac{a\sqrt 2+a\sqrt 2}{2a}$

$\frac{\overline{AC}+\overline{CB}}{\overline{AB}}=\frac{2a\sqrt 2}{2a}$

= $\sqrt 2$ (Ans)

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