True False With Reason

Question 12 Marks

Write the truth value (T/F) of the following with suitable reasons:
Sector is the region between the chord and its corresponding arc.

Answer

True.
Explanation:
It is given that sector is the region between the chord and its corresponding arc.
As we know that the region between the chord and its corresponding arc is called sector.

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Question 22 Marks

Write the truth value (T/F) of the following with suitable reasons:
If a circle is divided into three equal arcs each is a major arc.

Answer

True. Explanation: Given that if a circle is divided into three equal arcs each is a major arc. As we know that if points P, Q and R lies on the given circle C(O, r) in such a way that:$1\big(\widehat{\text{PQ}}\big)=1\big(\widehat{\text{QR}}\big)=1\big(\widehat{\text{RP}}\big)$
Then each arc is called major arc.

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Question 32 Marks

Write the truth value (T/F) of the following with suitable reasons:
Line segment joining the center to any point on the circle is a radius of the circle,

Answer

True.Explanation:
Given that line segment joining the centre to any point on the circle is a radius of the circle. As we know that line segment joining the centre to any point on the circle is a radius of the circle.

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Question 42 Marks

Write the truth value (T/F) of the following with suitable reasons:
A circle has only finite number of equal chords.

Answer

False.
Explanation:
It is given that a circle has only finite number of equal chords.
As we know that a circle having infinite number of unequal chords.

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Question 52 Marks

Write the truth value (T/F) of the following with suitable reasons:
A circle is a plane figure.

Answer

True.
Explanation:
Given that a circle is a plane figure.
As we know that a circle is a collection of those points in a plane that are at a given constant distance from a fixed point in the plane.

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Question 62 Marks

Write the truth value (T/F) of the following with suitable reasons:
The degree measure of a semi-circle is 180°

Answer

True. Explanation: Given that the degree measure of a semi-circle is 180°. As we know that the diameter ofa circle divides into two equal parts and each of these two arcs are known as semi-circle. $\widehat{\text{PQ}}$ and $\widehat{\text{QP}}$ are semi circle. Hence, $\text{m}\big(\widehat{\text{PQ}}\big)=\text{m}\big(\widehat{\text{QP}}\big)=180^\circ$

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Question 72 Marks

Write the truth value (T/F) of the following with suitable reasons:
A chord of a circle, which is twice as long is its radius is a diameter of the circle.

Answer

True.
Explanation:
Given that a chord of the circle, which is twice as long as its radius is diameter of the circle.
As we know that a chord of a circle which is largest to others and passing through the centre of the circle and twice as long as its radius is called diameter of the circle.

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Question 82 Marks

Write the truth value (T/F) of the following with suitable reasons:
The degree measure of an arc is the complement of the central angle containing the arc.

Answer

False.
Explanation:
Given that the degree measure of an arc is the complement of the central angle containing the arc.
As we know that the degree measure of a minor arc is the measure of the central angle containing the arc and that of a major arc is 360° minus the degree measure of the corresponding minor arc.
Let degree measure of an arc $\widehat{\text{PQ}}$ is $\theta$ of a given circle C(O, r) is denoted by $\text{m}\big(\widehat{\text{PQ}}\big)=\theta.$

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