Trigonometric Equations Question 257
Question: In a triangle $ ABC $ , if $ b+c=2a $ and $ \angle A=60{}^\circ , $ then $ \Delta ABC $ is
[MP PET 2004]
Options:
A) Scalene
B) Equilateral
C) Isosceles
D) Right angled
Show Answer
Answer:
Correct Answer: B
Solution:
We have, $ b+c=2a $ …..(i) $ \cos 60{}^\circ =\frac{a^{2}+c^{2}-b^{2}}{2ac} $
Þ $ \frac{1}{2}=\frac{4a^{2}-2bc-a^{2}}{2bc} $
Þ $ \frac{1}{2}=\frac{3a^{2}}{2bc}-1 $
Þ $ \frac{3}{2}=\frac{3a^{2}}{2bc} $
Þ $ bc=a^{2} $ ……(ii) From (i) and (ii), $ b=c=0 $ i.e., triangle is degenerate.
BETA
