GATE Electrical Engineering (EE) 2020 Solved Paper

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Question : 9 of 65

Marks: +1, -0

Given a semi-circle

{O}

as the center, as shown in the figure, the ratio

\;{\ov{ {AC}}+\ov{ {CB}}}/{ {A} \ov{ {B}}}

is

Where

\ov{ {AC}}, \ov{ {CB}} \;\;\& \;\;\ov{ {AB}}

are chords.

$√{2}$
$√{3}$
2
3

Solution:

Let radius of circle = r = AO = OB = OC

\ov{ {AC}}=√{r^{2}+r^{2}}=√{2} r=\ov{ {CB}}

\;{\ov{ {AC}}+\ov{ {CB}}}/{\ov{ {AB}}}=\;{√{2} r+√{2 r}}/{2 r}

=\;{2 √{2} r}/{2 r}=√{2}

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