Question

The largest and the shortest distances of the earth from the sun are r1 and r2. Its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun

Answer 1

Ans: (r1 + r2)/2

See diagram.

   Earth orbits around Sun in an Elliptical Orbit. Sun is at one of the two Foci. 

The major axis AB = AS + SB
                     = perihelion + aphelion
                     = r2 + r1 (given)

For an ellipse:   PS1 + PS2 = constant
        ∵   AS1 + AS2 = AB,   PS1 + PS2 = AB = r1 + r2

So When Earth P is at C,  
            
       CS1 + CS2 = AB 
       CS1 = CS2 = AB/2 = (r1 + r2)/2    Answer.
        (ΔC S2 S2  is Isosceles).

Answer 2

open images ...i hope this will help