Question

The angles of the triangle ABC satisfy the condition 2∠A+∠B=∠C. Inside this triangle, the point K is chosen on the bisector of the angle A such that BK=BC. Prove that ∠KBC=2∠KBA.

Answer 1

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Sum of roots sinA+sinB = c

a+b

= sinC

sinA+sinB

sin(A)+sin(B)[1− sinC1

]=0

sinC=1

C=90

0

.

Hence,

sinA+cosA=sinA+sinB

= a Aasin + b bsinB

= c

sinC(a+b)

= c

a+b

= c

a+b

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