KVPY 2019 SA Exam Previous Papers

Question : 65 of 80

Marks: +1, -0

Let ABC be a triangle in which AB = BC. Let X be a point on AB such that AX : XB = AB : AX. If AC = AX, then the measure of ∠ABC equals

Solution:

Let AC = b & AB = BC = a
Given

b/{a-b}=a/b

⇒ b^2 = a^2 -ab

⇒

b/a={-1+√5}/2

Let D be foot of perpendicular from B

\sin (∠ABD) =b/{2a}={√5-1}/4

⇒

∠ABD = 18º

∴ ∠ABC = 36°

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