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Square

ABCD is a squ...

Question

$A B C D$ is a square. A line $A X$ meets the diagonal $B D$ at $X$ and $A X = 2018 c m$ the length of $C X$ (in\ cm) is

A

125

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B

1009

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C

1000

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D

500

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Solution

The correct option is D $125$
$∠ C O D = 80$
$∠ B O X = 80$
as they are vertically opposite angles

diagonal of bisectors are at angle bisectors
$∠ O B X = 45$
exterior angle $= ∠ O X A$

exterior angle = sum of interior angle
$∠ O X A = 80 + 45$
$= 125$

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