Question

In the diagram \[O\] is the center of the circle with diameter \[20cm\] . The circle is the locus of the point X. State the distance of X from \[O\] .

A. \[5cm\]
B. \[8cm\]
C. \[10cm\]
D. \[20cm\]

Answer 1

Hint: A locus is nothing but a moving point. It is given that the given circle is formed by the locus of the point X. Thus, X is on the circle. Also given that the diameter of the given circle is \[20cm\] . We know that diameter is nothing but doubled the radius. Thus, the radius is half of the diameter.

Complete step by step answer:
It is given a circle which is formed by the locus of the point \[X\] . It is also given that the diameter of the circle is \[20cm\] .
Locus is nothing but the moving point. Here \[X\] is the locus thus it is the moving point. The path traced by \[X\] is nothing but the given circle. Since the circle is the path traced by the point \[X\] , it is on the circle. That is the point \[X\] is on the circle.
We know that the diameter of a circle has doubled the radius. That is let \[A\] be any circle and \[c\] be its center and \[r\] be its radius. Then, the diameter of this circle is given by \[d = 2r\] .
Let \[R\] be the radius of the given circle and \[D\] be the diameter of the given circle. Then \[D = 2R\] . It is given that the diameter of the given circle is \[20cm\] . Thus, \[20 = 2R\] we know that radius is nothing but half of the diameter.
 \[R = \dfrac{{20}}{2} = 10\]
Thus the radius of the circle is \[10cm\] .
Radius is nothing but the distance between the center of the circle to any point on the circle.
Here, \[X\] is any point on the circle and \[O\] is the center of the given circle. Thus, the distance between the point \[X\] and the center \[O\] is nothing but the radius of the given circle. Therefore, the distance between \[X\] and \[O\] is \[10cm\] .
Let us see the options, option (a) \[5cm\] this cannot be the right answer since we got the distance as \[10cm\]
Option (B) \[8cm\] this cannot be the right answer since we got the distance as \[10cm\] .
Option (C) \[10cm\] is the correct answer since we got the distance as \[10cm\] .
Option (D) \[20cm\] is not the correct answer since we got distance as \[10cm\] .
So, the correct answer is “Option C”.

Note: Radius can also be defined as the distance between the center of the circle to any point on the circle and diameter can be defined as the distance between the two opposite points on the circle. The diameter of a circle is also known as the largest chord of a circle.