Question 1 :
What is the common point of a tangent to a circle and the circle called?
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4b273b230584979917.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 sides AB and AC.
Question 3 :
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 4 :
From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
Question 5 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 7 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?
Question 8 :
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Does R bisects the arc PRQ?
Question 9 :
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 10 :
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 11 :
If a hexagon ABCDEF circumscribe a circle, is it TRUE or FALSE that AB + CD + EF = BC + DE + FA?
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 :
Is it TRUE or FALSE, that the angle between two tangents to a circle may be $0^{\circ}$?
Question 15 :
A tangent to a circle is a line that intersects the circle at only one point . TRUE or FALSE ?
Question 16 :
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 17 : <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 18 :
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 19 : <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 20 : <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 21 : <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 22 :
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 23 :
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 $90^{\circ}$, then OP = $a \sqrt{2}$ ?
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcc273b230584979a1b.JPG' />
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see the above image). Find the length TP.
Question 25 :
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 26 :
The tangent at any point of a circle is perpendicular to the radius through the point of contact . TRUE or FALSE ?
Question 27 :
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 28 :
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 29 :
State true or false. Lengths of tangents from an external point to a circle are equal.
Question 30 : <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 31 :
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 32 :
The tangents drawn at the ends of a diameter of a circle are ______.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b45273b230584979969.PNG' />
In the above figure, if PA and PB are tangents to the circle with centre O such that APB = $50^{\circ}$, then $\angle OAB$ is equal to
Question 34 :
If tangents PA and PB from a point P to a circle with centre O are inclined to each ofher at angle of 80°, then ∠ POA is equal to
Question 35 :
State true or false. A tangent to a circle is a straight line which touches the circle at only one point.
Question 36 : <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 38 :
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 39 : <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 40 :
Does a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A?
Question 41 : <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 42 :
A line and a circle in the same plane can co-exist in _______ different ways.
Question 43 :
State true or false. Only two tangents can be drawn to a circle from an external point.
Question 44 :
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 45 : <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 46 :
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 47 : <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 48 : <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 49 :
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 50 :
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 .
