Question

Sol. [Key Concept: With one vertex at $O$ and another on $ax - \sqrt{3}y = 0$, the third vertex has four possible positions (two lines × two sides).]

Possible ordinates of $C$ are ( 0 a) , ( $0, - a$ ),

$$\left( \frac{a\sqrt{3}}{2},\frac{- a}{2} \right),\left( \frac{- a\sqrt{3}}{2},\frac{a}{2} \right)$$

✔ (a) $(0,a)$ is one admissible third vertex.

✔ (b) $(\frac{\sqrt{3\ }a}{2}, - \frac{a}{2})$ is admissible.

✔ (c) $(0, - a)$ is admissible.

✔ (d) $( - \frac{\sqrt{3\ }a}{2},\frac{a}{2})$ is admissible.