Question

The diameters of a circle are___________

Answer 1

Hint: As we can see that this is a fill in the blank where we need to complete the sentence. The sentence seems to be a property of the diameter of a circle and it is to be filled by the name of that property.

Formula used:
The method used is the knowledge of concurrence and what concurrent lines are and how the diameters of a circle show the same property. That when some lines pass through the same point, they are said to be concurrent.

Complete step by step solution:
This blank can be filled by the term concurrent , that is the diameters of a circle are concurrent.
Now, we know that if two or more lines pass through a common point, or they intersect at a point, then the lines are said to be concurrent. This point of intersection is called the point of concurrence. As we know that all the diameters in a circle pass through a common point that is called the center of the circle. Hence, the center of the circle is the point of concurrence and the diameters of a circle are concurrent.

As we can see the figure, \[4\] diameters are passing through a common point \[O\], which is the point of concurrence.

Note: Alternatively, the diameters of a circle are congruent, i.e., they are of equal length. If the two lines have the same length, they are said to be congruent. Now since all the diameters are of equal length, they are congruent.