Answer
Verified
426.9k+ views
Hint: This type of question is solved by using the statement so if we prove that $AB$ and $CD$ are parallel then we will be able to validate the statements given in this question. As we realize that the line bisecting the chord and going through the focal point of the circle is opposite to the chord. So by using all this information, we can easily come to the point to choose the option.
Complete step-by-step answer:
Since in the question it is given that chords $AB$ and $CD$ are parallel.
So, we realize that the line bisecting the chord and going through the focal point of the circle is opposite to the chord.
First of all, we will assume $O$ be the point which will be the center of the circle. So in the figure, it will look like,
Hence, the angle $\angle OMA = \angle OND = {90^ \circ }$ each because of the alternate interior angles.
Hence, from this, we can say that $MN$ will definitely pass through the center of the circle.
As we can see here the line is passing through the center of the chords. So the chord will be bisected equally into two parts.
Hence, we can say that
$ \Rightarrow AM = MB$
And similarly, for the chord $CD$ , we have
$ \Rightarrow CN = ND$
Therefore, from this, we can say that $ON$ will be perpendicular to $CD$ and also similarly $OM$ will be perpendicular to $AB$ .
Hence from this, we can say that $MN$ is definitely perpendicular to both $AB$ and $CD$ .
Hence, the option $\left( c \right)$ is correct.
Note: A chord will be the line fragment and it joins two focuses on the boundary of a circle, and the chord which will be the longest of a circle is the width having the diameter. Since the breadth goes through and contains the focal point of the circle.
Complete step-by-step answer:
Since in the question it is given that chords $AB$ and $CD$ are parallel.
So, we realize that the line bisecting the chord and going through the focal point of the circle is opposite to the chord.
First of all, we will assume $O$ be the point which will be the center of the circle. So in the figure, it will look like,
Hence, the angle $\angle OMA = \angle OND = {90^ \circ }$ each because of the alternate interior angles.
Hence, from this, we can say that $MN$ will definitely pass through the center of the circle.
As we can see here the line is passing through the center of the chords. So the chord will be bisected equally into two parts.
Hence, we can say that
$ \Rightarrow AM = MB$
And similarly, for the chord $CD$ , we have
$ \Rightarrow CN = ND$
Therefore, from this, we can say that $ON$ will be perpendicular to $CD$ and also similarly $OM$ will be perpendicular to $AB$ .
Hence from this, we can say that $MN$ is definitely perpendicular to both $AB$ and $CD$ .
Hence, the option $\left( c \right)$ is correct.
Note: A chord will be the line fragment and it joins two focuses on the boundary of a circle, and the chord which will be the longest of a circle is the width having the diameter. Since the breadth goes through and contains the focal point of the circle.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Harsha Charita was written by A Kalidasa B Vishakhadatta class 7 social science CBSE
Which are the Top 10 Largest Countries of the World?
Banabhatta wrote Harshavardhanas biography What is class 6 social science CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE