Question 1 :
The tangent at any point of a circle is perpendicular to the radius through the point of contact . TRUE or FALSE ?
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4e273b230584979975.PNG' />
In the above figure, PQ is a chord of a circle and PT is the tangent at P such that $\angle QPT = 60^{\circ}$. Then $\angle PRQ$ is equal to
Question 3 :
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
Question 4 :
If two tangents inclined at an angle $60^{\circ}$ are drawn to a circle of radius 3 cm, then length of each tangent is equal to
Question 5 :
Is it TRUE or FALSE, that if a chord AB subtends an angle of $60^{\circ}$ at the centre of a circle, then angle between the tangents at A and B is also $60^{\circ}$?
Question 6 :
From a point Q , the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm . The radius of the circle is
Question 7 :
Is it TRUE or FALSE, that the tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC?
Question 8 :
Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, Is it TRUE or FALSE that BD = s – b?
Question 9 :
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. What is the radius of the inner circle?
Question 10 :
Do the tangents drawn at the ends of a chord of a circle make equal angles with the chord?
Question 11 :
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Question 12 :
If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
Question 13 :
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Question 14 :
State true or false. Tangent is perpendicular to the radius through the point of contact.
Question 15 :
Is it TRUE or FALSE, that the length of tangent from an external point on a circle is always greater than the radius of the circle?
Question 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcf273b230584979a1f.JPG' />
In the above image , XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. Then
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4f273b230584979977.PNG' />
According to the above figure, Is it TRUE or FALSE that PQL and PRM are tangents to the circle with centre O at the points Q and R, respectively and S is a point on the circle such that $\angle SQL = 50^{\circ}$ and $\angle SRM = 60^{\circ}$. Then $\angle QSR$ is equal to $40^{\circ}$?
Question 19 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcb273b230584979a19.PNG' />
In the above case, PQ is called a non-intersecting line with respect to the circle . TRUE OR FALSE ?
Question 20 :
Is it TRUE or FALSE, that the angle between two tangents to a circle may be $0^{\circ}$?
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4d273b230584979974.PNG' />
In the above figure, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is
Question 22 :
A tangent to a circle is a line that intersects the circle at only one point . TRUE or FALSE ?
Question 23 :
If a hexagon ABCDEF circumscribe a circle, is it TRUE or FALSE that AB + CD + EF = BC + DE + FA?
Question 24 :
Is it TRUE or FALSE, that the length of tangent from an external point P on a circle with centre O is always less than OP?
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcf273b230584979a1e.JPG' />
In the above figure , a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively . Find the side AB .
Question 26 :
In a right triangle ABC in which $\angle B = 90^{\circ}$, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Does the tangent to the circle at P bisects BC?
Question 27 :
A tangent to a circle intersects it in _____ point (s)
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979968.PNG' />
In the above figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of $50^{\circ}$ with PQ, then $\angle POQ$ is equal to
Question 29 :
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is
Question 30 :
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, what is the perimeter of the $\triangle ABC$?
Question 32 :
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
Question 33 :
The angle between the two tangents drawn from an external point to a circle is ______ to the angle subtended by the line-segment joining the points of contact at the centre.
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd1273b230584979a21.JPG' />
A quadrilateral ABCD is drawn to circumscribe a circle (see the above image) . Which of the following options are true ?
Question 35 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b43273b230584979966.PNG' />
In the above figure, AB is a chord of the circle and AOC is its diameter such that $\angle ACB = 50^{\circ}$. If AT is the tangent to the circle at the point A, then $\angle BAT$ is equal to
Question 36 :
Is it TRUE or FALSE that, If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ?
Question 37 :
Is it TRUE or FALSE, that AB is a diameter of a circle and AC is its chord such that $\angle BAC = 30^{\circ}$. If the tangent at C intersects AB extended at D, then BC = BD?
Question 38 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bca273b230584979a18.PNG' />
In the above case, we call the line PQ a tangent of the circle . TRUE OR FALSE ?
Question 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4c273b230584979972.PNG' />
In the above figure, The tangent at a point C of a circle and a diameter AB when extended intersect at P. If $\angle PCA=110^{\circ}$ , what is the value of $\angle CBA$?
Question 40 :
How many parallel tangents at the most can a circle have?
Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a49273b230584979914.PNG' />
In the above figure, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to
Question 42 :
If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, what is the area of the triangle?
Question 43 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b49273b23058497996f.PNG' />
In the above figure, tangents PQ and PR are drawn to a circle such that $\angle RPQ = 30^{\circ}$. A chord RS is drawn parallel to the tangent PQ. What is the value of $\angle RQS$?
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b42273b230584979965.PNG' />
In the above figure, if $\angle AOB = 125^{\circ}$, then $\angle COD$ is equal to
Question 45 :
If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Is it TRUE or FALSE that $AQ = \frac { 1 } { 2 } ( BC + CA + AB )$.
Question 46 :
Two concentric circles are of radii 5 cm and 3 cm . Find the length of the chord of the larger circle which touches the smaller circle .
Question 47 :
Is it TRUE or FALSE, that if angle between two tangents drawn from a point P to a circle of radius a and centre O is $60^{\circ}$, then OP = $a \sqrt {3}$ ?
Question 48 :
Is it TRUE or FALSE, that If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ?
Question 49 :
At any point on a circle there can be one and only one tangent .
TRUE OR FALSE?
Question 50 :
A line and a circle in the same plane can co-exist in _______ different ways.
