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GATE 2020 EE – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Given a semicircle with $O$ as the centre, as shown in the figure, the ratio $\dfrac{\overline{AC}+\overline{CB}}{\overline{AB}}$ is ________, where $\overline{AC}$, $\overline{CB}$ and $\overline{AB}$ are chords.

Diagram for GATE 2020 EE question 9
  1. $\sqrt2$
  2. $\sqrt3$
  3. 2
  4. 3

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Show answer and explanation

Correct answer: (A) $\sqrt2$

Explanation

C is the top of the semicircle, so $OA=OB=OC=r$ and the triangle $ACB$ is right-angled and isosceles, with $AC=CB=\sqrt2r$ and $AB=2r$. The ratio is $\frac{2\sqrt2r}{2r}=\sqrt2$.