KVPY 2016 SA Question 14

Consider a semicircle of radius 1 unit constructed on then diameter $AB$ , and let $O$ be its centre. Let $C$ be a point of $AO$ 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 $CD$ intersect at $H$ . Find the length $DH$ .

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