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The acute angle of a rhombus whose side ...

The acute angle of a rhombus whose side is a mean proportional between its diagonals is

A

`15^(@)`

B

`20^(@)`

C

`30^(@)`

D

`80^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the required angle be `'theta'`
`cos(pi-theta)=(a^(2)+a^(2)-d_(1)^(2))/(2a^(2))`
`rArr 2a^(2)-d_(1)^(2)=-2a^(2)cos theta`
`rArr d_(1)^(2)=4a^(2)"cos"^(2)(theta)/(2)`
`rArr d_(1)=2a cos.(theta)/(2)`
Similarly, `d_(2)^(2)=2a^(2)(1-cos theta)`
`rArr d_(2)=2a sin.(theta)/(2)`
Given , `a^(2)=d_(1)d_(2)`
`rArr a^(2)=4a^(2)sin.(theta)/(2)cos.(theta)/(2)`
`rArr theta = 30^(@)`
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