Question

Which geometric construction is shown here?

A)construct a circle given 3 points
B)construct the center of a given circle
C)construct the orthocenter of a triangle
D)construct the tangent to a point on the circle

Answer 1

Option B. construct the center of a given circle.

Explanation:

To determine the center of a given circle we will follow the following steps

1). We will draw a chord which intersects the circle at A and B.

2). We will construct perpendicular bisector of chord AB.

3). Similarly we will draw another chord CD and construct perpendicular bisector of CD.

4). As we know perpendicular from the center of a circle to any chord, bisects the chord. So we extend the perpendicular bisectors intersecting each other at point E.

Hence the intersection point E will be the center of the circle.

Option B. is the answer.

Answer 2

Option: B is the correct answer.

B) Construct the center of a given circle.

Explanation:

The center of the circle is constructed as:

• Draw a chord AB and construct it's perpendicular bisector.
• Draw another chord CD and construct it's perpendicular bisector.
• The point where the perpendicular bisectors of both the chord meet gives us the center of the given circle.

Hence, option B is correct we are given a geometric construction of center of a given circle.