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Maths True False[1 Marks ]

Circles · Jharkhand Board (JAC) STD 9 (Jharkhand - English Medium). 8 questions.

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True False[1 Marks ]

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8 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
Write the truth value $(T/F)$ of the following with suitable reasons: Sector is the region between the chord and its corresponding arc.
Answer
  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 21 Mark
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
 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 31 Mark
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
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 41 Mark
Write the truth value $(T/F)$ of the following with suitable reasons:
A circle has only finite number of equal chords.
Answer
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 51 Mark
Write the truth value $(T/F)$ of the following with suitable reasons: A circle is a plane figure.
Answer
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 61 Mark
Write the truth value $(T/F)$ of the following with suitable reasons: The degree measure of a semi-circle is $180^\circ $
Answer
Given that the degree measure of a semi-circle is $180^\circ .$ 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 71 Mark
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
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 81 Mark
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
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^\circ $ 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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