If ABC is a triangle and D is a point on side AB with AD=BD=CD, find the value of ∠ACB.
Answer:
90∘
- It is given that D is a point on the side AB of a △ABC such that AD=BD=CD. We are required to find the value of ∠ACB.
- We are given,
AD=CD⟹∠DAC=∠DCA (Angles opposite to equal sides of a triangle) …(1)
Also,
BD=CD⟹∠DBC=∠DCB (Angles opposite to equal sides of a triangle) …(2) - In △ABC,
∠BAC+∠ACB+∠CBA=180∘ [Angle sum property of a Triangle]⟹∠DAC+∠ACB+∠DBC=180∘⟹∠DCA+∠ACB+∠DCB=180∘ [By eq (1) and (2)]⟹∠ACB+∠ACB=180∘⟹2∠ACB=180∘⟹∠ACB=90∘ - Hence, the value of ∠ACB is 90∘.