1)find the sides of rectangle with greatest possible perimeter inscribed in a semicircle . . . .2)for what point P of the parobola ysq.=2px has the segment of inner normal at P the smallest length???

Dear sneha,

I recommend that you make a mirror image of the semicircle and the rectangle, flipping about the diameter. Than you will have a rectangle of double area inscribed into a full circle, and the question becomes : what rectangle inscribed into a circle has max area. The answer is the square, due to symmetry (I just restored that symmetry for you). So your initial rectangle inscribed into semicircle was [ r√2 ] x [ r/√2 ].

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Sagar Singh

B.Tech IIT Delhi