Question 1 :
State whether the given statement is true or false:- Two chords AB and CD of a circle are each at distances 4 cm from the centre, then AB = CD.
Question 2 :
If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.
Question 3 :
If two equal chords of a circle intersect within the circle, the line joining the point of intersection to the centre makes equal angles with the chords.TRUE or FALSE?
Question 4 :
If circles are drawn taking two sides of a triangle as diameters, the point of intersection of these circles do not lie necessarily on the third side. TRUE or FALSE ?
Question 5 :
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is
Question 6 :
The fixed point is called the ________ of the circle and the fixed distance is called the ________ of the circle.
Question 7 :
State whether the given statement is true or false:- Chords equidistant from the centre of a circle are equal in length.
Question 8 :
AC and BD are chords of a circle which bisect each other. ABCD is a ____________.
Question 9 :
If the non-parallel sides of a trapezium are equal, is it cyclic?
Question 10 :
If a circle is divided into three equal arcs, each is a major arc. TRUE or FALSE?
Question 11 :
In any triangle ABC, if the angle bisector of ∠A and perpendicular bisector of BC intersect, they intersect on the circumcircle of the triangle ABC. TRUE or FALSE?
Question 12 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a8f59b460d7261f49a.png' />
If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C andD, AB is __________ to CD.
Question 13 :
State whether the given statement is true or false:- The angles subtended by a chord at any two points of a circle are equal.
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a3f59b460d7261f494.png' />
In the above fig, the smaller segment is called the ______________________.
Question 15 :
State whether the given statement is true or false:- Two congruent circles with centres O and O′ intersect at two points A and B, then $\angle AOB=\angle AO'B$.
Question 16 :
State true or false: If the circumcentre of the triangle ABC is O. Then $\angle OBC+\angle BAC=90^{\circ}$.
Question 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a9f59b460d7261f49c.JPG' />
In the above fig, ∠ PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.
Question 18 :
The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. TRUE or FALSE?
Question 19 :
State whether the given statement is true or false:- A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.
Question 20 :
State Yes or No: AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre, then $4q^2=p^2+3r^2$ .
Question 21 :
A chord of a circle, which is twice as long as its radius, is a diameter of the circle. TRUE or FALSE?
Question 22 :
Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. The angles of the triangle DEF are 90°– mA, 90°– mB and 90°– mC. What is the value of m?
Question 23 :
The perpendicular from the centre of a circle to a chord does not bisect the chord. TRUE or FALSE?
Question 24 :
State Yes or No: An angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11ef59b460d7261f3d4.PNG' />
In the above figure, O is the centre of the circle, $\angle BCO=30^{\circ}$. Find x.
Question 26 :
State whether the given statement is true or false:- Two chords of a circle of lengths 10 cm and 8 cm are at the distances 8.0 cm and 3.5 cm, respectively from the centre.
Question 28 :
Either pair of opposite angles of a cyclic quadrilateral are _____________.
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d119f59b460d7261f3cc.PNG' />
In the above figure, $\angle ACB=40^{\circ}$. Find $\angle OAB$.
Question 30 :
Suppose you are given a circle. Can its centre be located by construction?
Question 31 :
If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic. TRUE or FALSE?
Question 32 :
State whether the given statement is true or false:- There is one and only one circle passing through three given non-collinear points.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d116f59b460d7261f3c8.PNG' />
In the above figure, $\angle AOB=90^{\circ}$ and $ \angle ABC=30^{\circ}$, then $\angle CAO$ is equal to
Question 34 :
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and $\angle ADC=140^{\circ}$, then $\angle BAC$ is equal to
Question 35 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d112f59b460d7261f3c2.PNG' />
In the above figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to
Question 36 :
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, it is a ____________.
Question 37 :
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
Question 38 :
The centre of a circle lies in ____________ of the circle.
Question 39 :
State Yes or No: A circle has radius $\sqrt{2}$ cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in major segment is $45^{\circ}$.
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d115f59b460d7261f3c6.PNG' />
In the above figure, if $\angle DAB=60^{\circ}$, $\angle ABD=50^{\circ}$, then $\angle ACB$ is equal to
Question 41 :
If the points lie on a line, then the third point will lie inside or outside the circle passing through the two points. TRUE or FALSE ?
Question 42 :
Two chords AB and AC of a circle subtends angles equal to $90^{\circ}$ and $150^{\circ}$, respectively at the centre. Find $\angle BAC$, if AB and AC lie on the opposite sides of the centre.
Question 43 :
AB and AC are two equal chords of a circle. State whether the bisector of the angle BAC passes through the centre of the circle or not.
Question 44 :
State whether the given statement is true or false:- Congruent arcs of a circle subtend equal angles at the centre.
Question 45 :
A quadrilateral ABCD is called _________ if all the four vertices of it lie on a circle.
Question 46 :
State True or False: Among all the chords of a circle passing through a given point inside the circle that one is smallest which is perpendicular to the diameter passing through the point.
Question 47 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d115f59b460d7261f3c7.PNG' />
In the above figure, BC is a diameter of the circle and $\angle BAO=60^{\circ}$. Then $\angle ADC$ is equal to
Question 48 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d113f59b460d7261f3c3.PNG' />
In the above figure, if $\angle OAB=40^{\circ}$, then $\angle ACB$ is equal to
Question 49 :
The line of centres of two intersecting circles subtends equal angles at the two points of intersection. TRUE or FALSE ?
Question 50 :
A circle is drawn with any side of a rhombus as diameter, does it pass through the point of intersection of its diagonals?
