Question 11 Mark
If A, B, C and D are four points such that $\angle\text{BAC}=45^\circ$ and $\angle\text{BDC}=45^\circ,$ then A, B, C, D are concyclic.
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Question 21 Mark
The degree measure of an arc is the complement of the central angle containing the arc.
Answer
View full question & 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 $\text{m}\big(\widehat{\text{PQ}}\big)=\theta.$
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 $\text{m}\big(\widehat{\text{PQ}}\big)=\theta.$
Question 31 Mark
A chord of a circle, which is twice as long is its radius is a diameter of the circle.
Answer
View full question & 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.
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.
Question 41 Mark
Two congruent circles with centres O and O′ intersect at two points A and B. Then $\angle\text{AOB}=\angle\text{AO'B}.$
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Question 51 Mark
Two chords AB and CD of a circle are each at distances 4cm from the centre. Then AB = CD.
Answer
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Question 61 Mark
If a circle is divided into three equal arcs each is a major arc.
Answer
View full question & 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.
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.
Question 71 Mark
Through three collinear points a circle can be drawn.
Answer
View full question & answer→False.
Solution:
Because, circle can pass through only two collinear points but not through three collinear points.
Solution:
Because, circle can pass through only two collinear points but not through three collinear points.
Question 81 Mark
A circle has only finite number of equal chords.
Answer
View full question & 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.
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.
Question 91 Mark
Line segment joining the center to any point on the circle is a radius of the circle,
Answer
View full question & 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.
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.
Question 101 Mark
The degree measure of a semi-circle is 180°
Answer
View full question & 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, $\text{m}\big(\widehat{\text{PQ}}\big)=\text{m}\big(\widehat{\text{QP}}\big)=180^\circ$
Hence, $\text{m}\big(\widehat{\text{PQ}}\big)=\text{m}\big(\widehat{\text{QP}}\big)=180^\circ$
Question 111 Mark
A circle is a plane figure.
Answer
View full question & 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.
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.
Question 121 Mark
If A, B, C, D are four points such that $\angle\text{BAC}=30^\circ$ and $\angle\text{BDC}=60^\circ$ then D is the centre of the circle through A, B and C.
Answer
View full question & answer→False.
Solution: Because, there can be many points D, such that $\angle\text{BDC}=60^\circ$ and each such point cannot be the centre of the circle through A, B and C.
Solution: Because, there can be many points D, such that $\angle\text{BDC}=60^\circ$ and each such point cannot be the centre of the circle through A, B and C.
Question 131 Mark
Sector is the region between the chord and its corresponding arc.
Answer
View full question & 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.
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.
Question 141 Mark
A circle of radius 3cm can be drawn through two points A, B such that AB = 6cm.
Answer
View full question & answer→True.
Solution:
Suppose, we consider diameter of a circle is AB = 66m.
Then, radius of a circle $=\frac{\text{AB}}{2}=\frac{6}{2}=3\text{cm},$ which is true.
Solution:
Suppose, we consider diameter of a circle is AB = 66m.
Then, radius of a circle $=\frac{\text{AB}}{2}=\frac{6}{2}=3\text{cm},$ which is true.
Question 151 Mark
If AOB is a diameter of a circle and C is a point on the circle, then AC2 + BC2 = AB2.
Question 161 Mark
ABCD is a cyclic quadrilateral such that $\angle\text{A}=90^\circ,\angle\text{B}=70^\circ,\angle\text{C}=95^\circ$ and $\angle\text{D}=105^\circ.$
Answer
View full question & answer→False.
Solution: In a cyclic quadrilateral, the sum of opposite angles is 180°. Now, $\angle\text{A}+\angle\text{C}=90^\circ+95^\circ=185^\circ\neq180^\circ$ and $\angle\text{B}+\angle\text{D}=70^\circ+105^\circ=175^\circ\neq180^\circ$ Here, we see that, the sum of opposite angles is not equal to 180°. So, it is not a cyclic quadrilateral.
Solution: In a cyclic quadrilateral, the sum of opposite angles is 180°. Now, $\angle\text{A}+\angle\text{C}=90^\circ+95^\circ=185^\circ\neq180^\circ$ and $\angle\text{B}+\angle\text{D}=70^\circ+105^\circ=175^\circ\neq180^\circ$ Here, we see that, the sum of opposite angles is not equal to 180°. So, it is not a cyclic quadrilateral.
Question 171 Mark
Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then $\angle\text{OAB}=\angle\text{OAC}.$
Answer
View full question & answer→False. Solution: In figure, AB and AC are two chords of a circle. Join OB and OC.
In $\triangle\text{OAB}$ and $\triangle\text{OAC},$ OA = OA [common side] OB = OC [both are the radius of circle] Here, we are not able to show that either the any angle or third side is equal and $\triangle\text{OAB}$ is, $\therefore\angle\text{OAB}\neq\angle\text{OAC}.$
In $\triangle\text{OAB}$ and $\triangle\text{OAC},$ OA = OA [common side] OB = OC [both are the radius of circle] Here, we are not able to show that either the any angle or third side is equal and $\triangle\text{OAB}$ is, $\therefore\angle\text{OAB}\neq\angle\text{OAC}.$
Question 181 Mark
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