Question

steps of a construction in a circle are described.

• step 1: draw a diameter of the circle and label two endpoints m and n, respectively.
• step 2: construct the perpendicular bisector of mn.
• step 3: label the points of intersection of the perpendicular bisector and the circle p and q, respectively.
• step 4: connect points m to p to n to q and back to m.

which figure is the result of this construction?
a. a square inscribed in the circle
b. an equilateral triangle inscribed in the circle
c. a non - square rhombus inscribed in the circle
d. a non - square rectangle inscribed in the circle

Explanation:

Step1: Recall properties of circle

A diameter is a line - segment passing through the center of the circle.

Step2: Understand perpendicular bisector

The perpendicular bisector of a diameter of a circle is also a diameter and is perpendicular to the first - drawn diameter.

Step3: Analyze angles and side - lengths

When we connect the four points \(M\), \(P\), \(N\), \(Q\) (end - points of two perpendicular diameters of a circle), the four line - segments \(MP\), \(PN\), \(NQ\), \(QM\) are equal in length (since they are all hypotenuses of right - angled triangles with the same legs, which are radii of the circle). Also, the angles between the sides are right angles because the diameters are perpendicular to each other.

Answer:

A. a square inscribed in the circle