Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a1f59b460d7261f492.png' />
In the above fig, the shorter arc is called the _____________.
Question 2 : <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 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d19ff59b460d7261f48f.png' />
In the above fig, segment PQ is the _________ of the circle.
Question 4 :
If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, then the chords are equal. True or False?
Question 5 :
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.
Question 6 :
If the non-parallel sides of a trapezium are equal, is it cyclic?
Question 7 : <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 8 :
The region between an arc and the two radii, joining the centre to the end points of the arc is called a _____________.
Question 9 :
State Yes or No: that two circles cannot intersect at more than two points.
Question 10 :
Equal chords of a circle subtend equal angles at the centre. TRUE or FALSE?
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d119f59b460d7261f3cd.PNG' />
In the above figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of $\angle ACD+\angle BED$.
Question 12 :
The line of centres of two intersecting circles subtends equal angles at the two points of intersection. TRUE or FALSE ?
Question 13 : <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 14 :
State true or false: If a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals are also equal.
Question 15 :
If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.
Question 16 : <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 17 :
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 18 :
ABC and ADC are two right triangles with common hypotenuse AC. Is ∠ CAD = ∠ CBD?
Question 19 :
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 20 :
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 21 : <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 22 :
Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Is BP = BQ?
Question 23 : <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 24 :
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 25 : <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 26 :
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 27 :
Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Question 28 :
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 29 :
The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a4f59b460d7261f496.png' />
In the above fig, AB is a diameter of the circle, CD is a chord equal to the radius of the circle. AC and BD when extended intersect at a point E. Find ∠ AEB.
