Question 1 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bce273b230584979a1d.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 AC.

Question 2 : State true or false. A tangent to a circle is a straight line which touches the circle at only one point.

Question 3 : In two concentric circles , the chord of the larger circle , which touches the smaller circle , is bisected at the point of contact . Is this statement true ?

Question 4 : A line intersecting a circle in two points is called a _______.

Question 5 : If angle between two radii of a circle is $130^{\circ}$, the angle between the tangents at the ends of the radii is :

Question 6 : 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 7 : Is it TRUE or FALSE, that the angle between two tangents to a circle may be $0^{\circ}$?

Question 8 : <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 9 : <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 11 : 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 12 : <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 13 : At any point on a circle there can be one and only one tangent . TRUE OR FALSE?

Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b46273b23058497996a.PNG' /> In the above figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and $\angle BQR = 70^{\circ}$, then $\angle AQB$ is equal to

Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd0273b230584979a20.JPG' /> In the above figure , if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ$ = $110^{\circ}$ , then $\angle PTQ$ is equal to

Question 16 : What is a line intersecting a circle in two points called?

Question 17 : Does a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A?

Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979967.PNG' /> In the above figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $\angle OTA = 30^{\circ}$. Then AT is equal to

Question 19 : <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 20 : 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 21 : The common point of a tangent to a circle and the circle is called point of contact.

Question 22 : <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 23 : The opposite sides of a quadrilateral circumscribing a circle subtend ________ angles at the centre of the circle.

Question 24 : <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 25 : Two concentric circless are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle

Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcd273b230584979a1c.JPG' /> The above image shows that a circle and two lines parallel to a given line AB is such that one is a tangent and the other , a secant to a circle , i.e , the line CD is the tangent at point M while the line EF is the secant . Is this statement true ?

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/61b19bcc273b230584979a1a.JPG' /> The above image represents two tangents TP and TQ drawn to a circle with centre O from an external point T . Then

Question 29 : <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 30 : State true or false. Only two tangents can be drawn to a circle from an external point.

Question 31 : Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?

Question 32 : Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?

Question 33 : 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 34 : <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 35 : 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 36 : Two circles with centres O and $O ^ { \prime }$ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and $O ^ { \prime }P$ are tangents to the two circles. What is the length of the common chord PQ?

Question 37 : State true or false. Tangent is perpendicular to the radius through the point of contact.

Question 38 : 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 39 : 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 40 : At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is

Question 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4b273b230584979916.jpg' /> In the above figure, 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. ∠ AOB = ?

Question 42 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4f273b230584979976.PNG' /> According to the above figure, Is it TRUE or FALSE that BOA is a diameter of a circle and the tangent at a point P meets BA extended at T. If $\angle PBO = 30^{\circ}$, then $\angle PTA$ is equal to $30^{\circ}$?

Question 43 : From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, what is the perimeter of the triangle PCD?

Question 44 : 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 45 : <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 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4b273b230584979971.PNG' /> In the above figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, what is the length of AB?

Question 47 : 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 48 : 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 49 : The tangent at any point of a circle is perpendicular to the radius through the point of contact . TRUE or FALSE ?

Question 50 : 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?