GATE Electrical 2020 | GA Question: 9

Question

Given a semicircle with $\text{O}$ 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.

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $2$
• D. $3$

Answer 1

Ans A

Given O as the center. AB is the diameter. Let Diameter = $2r$

Then $ AO = OB = r $, $ CO = r $ Semicircle.

$\angle COB = \angle COA= 90^{\circ}$, Applying Pythagoras Theorem in $\triangle COB, \triangle COA$

$CB = CA = \sqrt{2}r$

Putting in given equation.$\frac{\overline{AC }+ \overline{CB}}{\overline{AB}} = \frac{\sqrt{2}r +\sqrt{2}r }{2r} = \frac{2\sqrt{2}r }{2r} = \frac{\sqrt{2} }{1}=\sqrt{2}$