    Question

# In triangle ABC,AD and BE are the medians drawn through the angular points A and B respectively. If ∠DAB=2∠ABE=360 and AD=6 units, then circumradius of the triangle is equal to (where A,B,C are angles opposite to the sides BC,CA,AB respectively)

A
(35)cosecC
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B
(3+5)cosecC
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C
2(35)cosecC
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D
2(3+5)cosecC
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Solution

## The correct option is B (3+√5)cosecCLet G be the centroid, then AG=4 and ∠AGB=126∘ ∴In ΔAGB,4sin18∘=csin126∘4sin18∘=ccos36∘ ⇒c=4(cos36∘sin18∘)=6+2√5⋯(i) ∵sin18∘=14(√5−1),cos36∘=14(√5+1) Now csinC=2R ⇒R=12csinC Putting value of c from equation (i) ⇒R=(√5+3)cosecC  Suggest Corrections  0      Similar questions
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