KVPY Government Jobs Exams

In triangle ABC, let AD, BE and CF be the internal angle bisectors with D, E and F on the sides BC, CA and AB
respectively. Suppose AD, BE and CF concur at I and B, D, I, F are concyclic, then ∠IFD has measure

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KVPY Other Question

If a, b, c, d are positive real numbers such that
6
a b c d
5
a b c
4
a b
3
a + + +
=
+ +
=
+
= , then
b 2c 3d
a
+ +
is A regular octagon is formed by cutting congruent isosceles right- angled triangles from the corners of a square. If
the square has side- length 1, the side - length of the octagon is