Question 1 :
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 3 : <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 4 :
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 5 :
State true or false. Lengths of tangents from an external point to a circle are equal.
Question 6 :
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 7 :
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 8 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?
Question 9 :
If angle between two radii of a circle is $130^{\circ}$, the angle between the tangents at the ends of the radii is :
Question 10 : <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 11 :
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 12 :
State true or false. A tangent to a circle is a straight line which touches the circle at only one point.
Question 13 :
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Is QORP is a cyclic quadrilateral?
Question 14 :
The opposite sides of a quadrilateral circumscribing a circle subtend ________ angles at the centre of the circle.
Question 15 : <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 16 :
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 17 : <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 18 :
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 19 :
What is a line intersecting a circle in two points called?
Question 20 : <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 21 :
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 22 :
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 24 :
The tangents drawn at the ends of a diameter of a circle are ______.
Question 25 : <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 27 :
A tangent to a circle is a line that intersects the circle at only one point . TRUE or FALSE ?
Question 28 :
The tangent at any point of a circle is perpendicular to the radius through the point of contact . TRUE or FALSE ?
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 :
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 31 :
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 32 : <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 33 :
Is it TRUE or FALSE, that the angle between two tangents to a circle may be $0^{\circ}$?
Question 34 : <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 35 :
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 36 : <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 37 : <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 38 :
How many parallel tangents at the most can a circle have?
Question 39 :
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 40 :
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.
