Question 1 :
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^{\circ}$, then $\angle POA$ is equal to
Question 2 :
A tangent to a circle intersects it in _____ point (s)
Question 3 : <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 4 : <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 5 :
What is a line intersecting a circle in two points called?
Question 6 :
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 7 :
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 8 : <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 9 :
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 10 :
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 11 :
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 13 :
At any point on a circle there can be one and only one tangent .
TRUE OR FALSE?
Question 14 :
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 15 : <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 16 :
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 17 : <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 18 : <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 19 :
State true or false. Only two tangents can be drawn to a circle from an external point.
Question 20 : <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 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 :
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 23 : <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 24 : <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 25 :
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 26 :
If angle between two radii of a circle is $130^{\circ}$, the angle between the tangents at the ends of the radii is :
Question 27 :
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 28 :
A line intersecting a circle in two points is called a _______.
Question 29 : <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.
