Polygons and Circles Question 3

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?

Acute triangle

Equilateral triangle

Isosceles triangle

Right triangle

Scalene triangle

Approach

A triangle is isosceles if two sides are equal. Since both triangles have two sides that are radii, they must both be isosceles.

Isosceles triangles have the property where the angles opposite of the equal sides are congruent as well.

The triangle on the left will have angles of $60^\circ$ , $60^\circ$ , and $60^\circ$ . It is therefore an equilateral triangle.

The triangle on the left will have angles of $90^\circ$ , $45^\circ$ , and $45^\circ$ . It is a right isosceles triangle.

We do not have a scalene triangle, a triangle with three different length sides.