Question

Choose the correct word that completes each statement about inscribing a square in a circle. The second diameter that is constructed or copied is to the first diameter. The chord that connects the endpoints of the diameters forms a(n) triangle. The side of the inscribed square has a length equal to the radius, r.

Answer 1

1. Perpendicular

2. Isosceles

3. Never

Answer 2

The second diameter that is constructed or copied is perpendicular to the first diameter.

Basically because the diameters of a square are related as perpendicular bisectors to each other. That is, they are perpendicular and the intersect at the midpoint of each one.

The chord that connects the endpoints of the diameters forms an isosceles triangle.

The chords that go from each endpoint of the diameters form an isosceles triangle due to the summetry of the figure, because the pair of diameters divide the circle in equal parts, making the chords to create this symmetry to define isosceles triangles.

The side of the inscribed square has a length never equal to the radius, r.

Now, it's important to know that the inscribed square doesn't match the radius, that is, each chord represents each side of the square, which means those sides are never equal to the radius.