Suppose n≥0 is an integer and all the roots of x³+bx+4-(2×2016ⁿ)=0 are integers . Find all possible b.

Let ABC be a ∆ with circumcircle £ and in centre I. Let internal angle bisectors of ∆ ABC meet £ at A',B',C'. respectively. Let B'C' intersect AA'in P and AC in Q,and let BB' intersect AC in R.
Suppose the quadrilateral PIRQ is a kite I.e. IP=IR AND QP=QR.
PROVE that ∆ ABC is equilateral.

Q.)  The present ages of two brothers A AND B and their father are 3 distinct positive integers a,b,c respectively.
Suppose (b-1)/a-1 and (b+1)/a+1 are two consecutive integers and (c-1)/b-1 and (c+1)/b+1 are two consecutive integers . If  a+b+c≤150 determine a,b,c.

Let ABC be an isosceles ∆ with AB=AC. Let ¶ represent the circumcirle of ∆ABC and O be the centre of circle .Let CO meet ¶ in D.Draw a line parallel to AC through D .
Let it intersect AB at E. Suppose AE:EB=2:1.
PROVE THAT ABC IS EQUILATERAL ∆.

(Hint: you may join BD and DA. And extend DE to BC at F.

Hello friends..   Here's one more interesting question on GEOMETRY.. .         
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