Question 1 : <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 2 :
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 3 : <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 4 :
If a hexagon ABCDEF circumscribe a circle, is it TRUE or FALSE that AB + CD + EF = BC + DE + FA?
Question 5 :
State true or false. Only two tangents can be drawn to a circle from an external point.
Question 6 :
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 7 :
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 8 :
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 9 :
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 10 :
State true or false. A tangent to a circle is a straight line which touches the circle at only one point.
Question 12 :
Is it TRUE or FALSE, that the angle between two tangents to a circle may be $0^{\circ}$?
Question 13 :
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 14 : <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 15 :
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 16 :
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 17 :
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 18 :
The tangents drawn at the ends of a diameter of a circle are ______.
Question 19 : <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 20 :
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 22 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 23 :
State true or false. Lengths of tangents from an external point to a circle are equal.
Question 24 :
Do the tangents drawn at the ends of a chord of a circle make equal angles with the chord?
Question 25 :
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 26 :
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 27 :
How many parallel tangents at the most can a circle have?
Question 28 :
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 29 :
A tangent to a circle intersects it in _____ point (s)
Question 30 :
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 31 :
A tangent to a circle is a line that intersects the circle at only one point . TRUE or FALSE ?
Question 32 :
The lengths of tangents drawn from an external point to a circle are equal . TRUE or FALSE ?
Question 33 : <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 34 : <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 35 : <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 36 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?
Question 37 :
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 38 :
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 39 :
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 40 :
A tangent to a circle intersects it in how many point(s)?
Question 41 :
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 42 : <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 43 : <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 44 : <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 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
