Question 1 :
Segment of a circle is the region between an arc and _____________ of the circle.
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d118f59b460d7261f3cb.PNG' />
In the above figure, $\angle ADC=130^{\circ}$ and chord BC = chord BE. Find $\angle CBE$.
Question 3 : <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 4 :
If two arcs are congruent, then their corresponding chords are equal. TRUE or FALSE?
Question 5 : <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 6 :
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 8 :
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 9 :
State true or false: If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals are also equal.
Question 10 :
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 11 :
The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. TRUE or FALSE?
Question 12 :
If a circle is divided into three equal arcs, each is a major arc. TRUE or FALSE?
Question 13 :
State True or False: If two chords of a circle are equal, then their corresponding arcs are congruent and conversely, if two arcs are congruent, then their corresponding chords are equal.
Question 14 :
ABC and ADC are two right triangles with common hypotenuse AC. Is ∠ CAD = ∠ CBD?
Question 15 :
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 16 :
AC and BD are chords of a circle which bisect each other. AC and BD are diameters. TRUE or FALSE ?
Question 17 :
State true or false: If the circumcentre of the triangle ABC is O. Then $\angle OBC+\angle BAC=90^{\circ}$.
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11ff59b460d7261f3d5.PNG' />
In the above figure, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD respectively. If $\angle POQ=150^{\circ}$, then $\angle APQ$ is equal to
Question 19 :
Equal chords of a circle (or of congruent circles) are not necessarily equidistant from the centre (or centres). TRUE or FALSE?
Question 20 : <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 21 :
A quadrilateral ABCD is called _________ if all the four vertices of it lie on a circle.
Question 22 :
If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic. TRUE or FALSE?
Question 23 :
If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, state whether the two chords are non-parallel or not.
Question 24 : <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 25 : <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 26 :
State Yes or No: If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then PA is angle bisector of $\angle BPC$.
Question 27 :
State whether the given statement is true or false:- If A, B, C, D are four points such that $\angle BAC=30^{\circ}$ and $\angle BDC=60^{\circ}$, then D is the centre of the circle through A, B and C.
Question 28 :
State true or false: O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Then $\angle BOD\ =\ \angle A$.
Question 29 :
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
Question 30 :
Given an arc of a circle, can the circle be completed?
Question 32 :
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 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11cf59b460d7261f3d0.PNG' />
State Yes or No: In the above figure, if two chords AB and CD of a circle AYDZBWCX intersect at right angles, Then arc CXA + arc DZB = arc AYD + arc BWC = semicircle.
Question 34 :
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 35 : <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 36 :
State whether the given statement is true or false:- If A, B, C and D are four points such that $\angle BAC=45^{\circ}$ and $\angle BDC=45^{\circ}$, then A, B, C, D are concyclic.
Question 37 :
State whether the given statement is true or false:- Angles in the same segment of a circle are equal.
Question 38 : <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 39 :
State true or false: ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Then $\angle CBD\ +\ \angle CDB\ =\frac{1}{2}\angle BAD$.
Question 40 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d11af59b460d7261f3ce.PNG' />
In the above figure, $\angle OAB=30^{\circ}$ and $\angle OCB=57^{\circ}$. Find $\angle BOC$.
Question 41 : <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 42 : <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 43 :
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 44 :
State whether the given statement is true or false:- Two chords AB and AC of a circle with centre O are on the opposite sides of OA, then $\angle OAB=\angle OAC$.
Question 45 :
If two circles intersect at two points, their centres lie on the perpendicular bisector of the common chord. TRUE or FALSE?
Question 46 :
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 47 :
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 48 :
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 49 :
The length of the complete circle is called its circumference. TRUE or FALSE?
Question 50 :
Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?
