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Question

If ABCD is a cyclic quadrilateral inscribed in a circle of radius 2 units such that AB=1, BD=23 then AD=


  1. 35+12

  2. 352

  3. 3512

  4. 5+12


Solution

The correct option is A

35+12


Let AD=x and BAD=θ

By Sine Rule, inΔBAD, BDsinθ=2R

sinθ=232×2sinθ=32 θ=60

By Cosine Rule, in ΔBAD, cos60=x2+12(23)22×x×1

 x=1±352

x>0 x=1+352

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