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Consider a semicircle of radius 1 unit c...

Consider a semicircle of radius 1 unit constructed on the diameter AB, and let O be its centre. Let C be a point on AO such that AC : CO = 2:1. Draw CD perpendicular to AO with D on the semicircle. Draw OE perpendicular to AD with E on AD. Let OE and CD intersects at H. Then DH equals

A

`1/sqrt5`

B

`1/sqrt3`

C

`1/sqrt2`

D

`(sqrt5-1)/2`

Text Solution

Verified by Experts

The correct Answer is:
c
E is mid point of AD.
theta`cos2theta=1/3 Rightarrowcos^(2)theta-1=1/3`
`cos^(2)theta=2/3`
`costheta(sqrt2)/sqrt3`
`sintheta= sqrt(1-2/3)=1/sqrt3`
`(ED)/1=1/sqrt3`
`DH=EDsec theta`
`1/sqrt3xxsqrt3/sqrt2`
`1/sqrt2`
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