Two dimensional projectile motion

1. The problem statement, all variables and given/known data
A regular hexagon of side a=10√3 m is kept at horizontal surface as shown in the figure. A particle is projected with velocity V m/s at an angle θ from point k such that it will just touch the all four corners B,C,D,E. If O is the centre of hexagon and x-axis is parallel to horizontal and y-axis is perpendicular to AF and CD sides of hexagon then answer the following

A) Velocity of projectile at maximum height

3. The attempt at a solution
Let k be the origin. R be the range of projectile
Coordinates of B = (R/2 – a, a√3/2)
Coordinates of C = (R/2 – a/2, a√3)
Equation of trajectory : [itex]y=x \tan \theta \left(1-\dfrac{x}{R} \right) [/itex]

Satisfying the above coordinates does not give me the right answer.

Attached Images
File Type: jpg 20140423_113328.jpg (40.2 KB)

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