Question

If a chord subtends 120${}^{\circ }$ at the center of the circle. What can be said about the largest triangle inscribed in a circle by taking chord as the base?

• A. Square
• B. Rectangle
• C. Parallelogram
• D. Trapezium

Answer 1

The correct option is A

Square

Let O be the center of the circle and the chord be AB

The largest Triangle inscribed in that circle taking base AB is formed when the altitude of that triangle passes through the center of the circle.

and angle subtended at the circumference = 60${}^{\circ }$ (half of 120${}^{\circ }$)

Thus making it an equilateral triangle.