Q66 / 150 · MHT CET 2022 (08 Aug Shift 1) · Mathematics
With usual notations in $\triangle A B C$ if $a^2+b^2-c^2=a b$, then measure of angle $C$ is
- A$\frac{\pi}{4}$
- B$\frac{\pi}{6}$
- C$\frac{\pi}{2}$
- Correct answerD$\frac{\pi}{3}$
Solution
$\begin{aligned} & a^2+b^2-c^2=a b \\ & \Rightarrow \frac{a^2+b^2-c^2}{2 a b}=\frac{1}{2} \\ & \Rightarrow \cos c=\frac{1}{2} \\ & \Rightarrow c=\frac{\pi}{3}\end{aligned}$
Hence, the correct answer is option: 'D'.