Maths-
General
Easy
Question
In the figure, AB = AC,
and
Then

- BC > CD
- BC = CD
- BC < CD
- cannot decide
The correct answer is: BC = CD
We should find relation between BC and CD
Given, AB = AC
∠ABC=∠ACB=x (Isosceles triangle property)
In △ABC
∠ABC+∠ACB+∠ABC=180 (Sum of angles of triangle)
x+x+48=180
2x=132
x=66∘
∠BCA=∠BCD+∠DCB=66
∠BCD=66−18
∠BCD=48∘
Now, In △BCD
Sum of angles of triangle = 180
∠BCD+∠BDC+∠DBC=180
48+∠BDC+66=180
∠BDC=66∘
Since, ∠BDC=∠DBC
hence, BD=CD (Isosceles triangle property)
Thus, △BDC is an isosceles triangle.
Hence BC=CD
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