Question

1. in the figure below, a, b, c, and d lie on the circle centered at o. which of the following does not appear in the figure? a. acute triangle b. equilateral triangle c. isosceles triangle d. right triangle e. scalene triangle

Explanation:

1. Analyze triangle types:

• In $\triangle AOB$, since $OA = OB$ (radii of the circle) and $\angle AOB=60^{\circ}$, $\triangle AOB$ is an equilateral triangle (an equilateral triangle is also an acute - angled and isosceles triangle).
• In $\triangle DOC$, $\angle DOC = 90^{\circ}$, so it is a right - angled triangle. Also, since $OD = OC$ (radii of the circle), it is an isosceles right - angled triangle.
• A scalene triangle has no equal sides. In the given figure, all triangles formed using the radii have at least two equal sides (the radii of the circle), so there is no scalene triangle.

Answer:

E. Scalene triangle