(a) 4ABC exists such that AD : DB = 1 : 2, where D is a point on side AB. Similarly, a
point E exists on side AC such that ∠BEC = ∠BDC. Find the ratio of ∠BED to ∠BCD.
(b) 4ABC is an equilateral triangle having side length 1 unit. 4BDC is isosceles with
DB = DC, where point D lies outside 4ABC and ∠BDC = 120◦
. If points M and N lie on AB
and AC respectively such that ∠MDN = 60◦
, find the perimeter of 4AMN.
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