Question 1 :
AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is
Question 2 : <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 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d113f59b460d7261f3c4.PNG' />
In the above figure, if AOB is a diameter of the circle and AC = BC, then $\angle CAB$ is equal to
Question 4 : <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 5 :
State whether the given statement is true or false:- Through three collinear points a circle can be drawn.
Question 6 :
State whether the given statement is true or false:- If AOB is a diameter of a circle and C is a point on the circle, then $AC^2+BC^2=AB^2$.
Question 7 :
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 8 :
State true or false: If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals are also equal.
Question 9 :
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
Question 10 :
A, B and C are three points on a circle. State whether that the perpendicular bisectors of AB, BC and CA are concurrent or not.
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11bf59b460d7261f3cf.PNG' />
In the above figure, $\angle OAB=30^{\circ}$ and $\angle OCB=57^{\circ}$. Find $\angle AOC$.
Question 12 :
A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and $\angle ADC=130^{\circ}$. Find $\angle BAC$.
Question 13 :
State Yes or No: If two equal chords AB and CD of a circle when produced intersect at a point P then PB = PD.
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11df59b460d7261f3d2.PNG' />
In the above figure, O is the centre of the circle, $\angle BCO=30^{\circ}$. Find y.
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11cf59b460d7261f3d1.PNG' />
State Yes or No: In the above figure, AB and CD are two chords of a circle intersecting each other at point E. Then $\angle AEC=\frac{1}{2\ }$ (Angle subtended by arc CXA at centre + angle subtended by arc DYB at the centre).
Question 16 :
State true or false: If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, then P, Q, R and D are concyclic.
Question 17 :
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 18 :
State whether the given statement is true or false:- Congruent arcs of a circle subtend equal angles at the centre.
Question 19 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d120f59b460d7261f3d6.PNG' />
In the above figure, two congruent circles have centres O and O′. Arc AXB subtends an angle of $75^{\circ}$ at the centre O and arc A′YB′ subtends an angle of $25^{\circ}$ at the centre O′. Then the ratio of arcs AXB and A′YB′ is
Question 20 :
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 21 :
The diameter divides the circle into 2 equal halves called ____________.
Question 22 :
The length of the complete circle is called its circumference. TRUE or FALSE?
Question 25 :
The region between an arc and the two radii, joining the centre to the end points of the arc is called a _____________.
Question 26 : <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 27 :
The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle. TRUE or FALSE?
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a0f59b460d7261f490.png' />
In the above fig, segment AB is the _____________ of the circle.
Question 30 :
The distance of a line from a given point is found out by calculting the length of the perpendicular from the point to the line. TRUE or FALSE?
Question 31 :
If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle. TRUE or FALSE?
Question 32 :
The angle subtended by an arc at the centre is __________ the angle subtended by it at any point on the remaining part of the circle.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a5f59b460d7261f497.png' />
In the above fig, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠ DBC = 55° and ∠ BAC = 45°, find ∠ BCD.
Question 34 :
A chord of a circle, which is twice as long as its radius, is a diameter of the circle. TRUE or FALSE?
Question 35 :
The centre of a circle lies in ____________ of the circle.
Question 36 :
A circle has only finite number of equal chords. TRUE or FALSE?
Question 37 :
If a circle is divided into three equal arcs, each is a major arc. TRUE or FALSE?
Question 38 :
If chords of congruent circles subtend equal angles at their centres, then the chords are not necessarily equal. TRUE or FALSE?
Question 39 :
Suppose you are given a circle. Can its centre be located by construction?
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1aaf59b460d7261f49e.png' />
In the above fig, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.
Question 41 :
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC is 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD.
Question 42 :
ABC and ADC are two right triangles with common hypotenuse AC. Is ∠ CAD = ∠ CBD?
Question 43 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a8f59b460d7261f49b.JPG' />
In the above fig, A, B and C are three points on a circle with centre O such that ∠ BOC = 30° and∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1aaf59b460d7261f49d.JPG' />
In the above fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.
Question 45 :
The line of centres of two intersecting circles subtends equal angles at the two points of intersection. TRUE or FALSE ?
Question 46 :
AC and BD are chords of a circle which bisect each other. AC and BD are diameters. TRUE or FALSE ?
Question 47 :
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 48 :
Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.
Question 49 :
ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Is AE = AD?
Question 50 :
Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. ∠ABC is equal to ___________ the difference of the angles subtended by the chords AC and DE at the centre.
