Published by:
CGP EDU Academic Team
Published on: August 13, 2026
In a Δ ABC, ∠ C = 60° and ∠ A = 75°. If D is a point on AC such that the area of the Δ BAD is 
times the area of the Δ BCD, find the ∠ ABD.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
ABD = 30°
Sol. 
Area of Δ BAD = 
× Area of Δ BCD
⇒ 
BD × BA sin θ = 
× 
BC × BD sin (45º – θ )
= 
.............(1)
From Sine-Rule
= 
∴ 
= 
= 
∴ From equation (1)
= 
⇒ 
= cot θ –1 ⇒ 
= cot θ – 1
⇒ cot θ = 
⇒ θ = 30º ⇒ ∠ ABD = 30º
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