What is the property of the angle between the radius and the tangent at the point of contact with a circle?

The angle is always 90°.

In the construction of a tangent from an exterior point, if PA and PB are the tangents, what relationship do they hold?

The lengths of the tangents are equal, so PA = PB.

To construct the circumcircle of a triangle, which lines must be drawn first?

The perpendicular bisectors of any two sides of the triangle.

The circumcentre of a triangle is equidistant from which points?

The circumcentre is equidistant from all three vertices of the triangle.

To find the incentre of a triangle, which geometric constructs are used?

The angle bisectors of any two angles of the triangle.

Fill in the blank: The circumradius of an equilateral triangle is equal to its side length divided by ___ .

√3

True or False: The radius of the inscribed circle of a regular hexagon is equal to the length of its sides.

True.

What is the formula for the interior angle of a regular hexagon?

The formula is [(2n - 4) / n] × 90°, where n = 6.

What is the relationship between the radius of the circumcircle and the side length in a regular hexagon?

The radius of the circumcircle equals the side length.

Fill in the blank: In constructing the inscribed circle of a triangle, the incentre is located at the intersection of the ___ .

Angle bisectors

True or False: The lengths of the tangents from a point to a circle can be different.

False. The lengths are always equal.

In the construction of tangents from a point outside the circle, what is the first circle you draw?

A circle with diameter OP, where O is the center of the circle and P is the external point.

What geometric figure is created when drawing the perpendicular bisectors of a triangle's sides?

The circumcentre of the triangle.

Fill in the blank: The radius used to draw the circumcircle of a triangle is the distance from the circumcentre to any vertex, denoted as ___.

OA (or OB or OC)

What is the significance of the point where the angle bisectors of a triangle intersect?

It is the incentre, which is equidistant from all three sides of the triangle.