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CGP EDU Academic Team
Published on: August 13, 2026
In a scalene triangle ABC, D is a point on the side AB such that CD 2 = AD. DB, if sinA. sinB = sin 2 
then prove that CD is internal bisector of ∠ C.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let ∠ ACD = α ⇒ ∠ DCB = (C – α )
Figuire
Applying the sine rule in Δ ACD and in Δ DCB respectively, we get
⇒ 
and 
⇒ 
⇒ 
[cos(2 α – C) – cosC] = sin 2 
⇒ 
[cos(2 α – C) – 1 + 2sin 2 
] = sin 2 
⇒ cos(2 α – C) = 1
⇒ α = 
Thus, CD is the internal angle bisector of angle C.
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