In a parallelogram ABCD, the bisector of ∠ABC intersects AD at E. If ED = 5, BE = 6, CE = 6, find AB?
A
8
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B
4
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C
9
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D
6
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Solution
The correct option is B 4 In ΔCBE, using sine rule =5+xsin(180∘−2θ)=6sinθ ⇒cosθ=5+x12 In ΔABE,cosθ=x2+36−x212x ⇒3612x=5+x12⇒x2+5x−36=0 ⇒(x+9)(x−4)=0 ⇒x=4