Question 1 :
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 2 :
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 3 :
<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 4 :
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 5 :
State true or false. Tangent is perpendicular to the radius through the point of contact.

Question 6 :
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 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/61b19bcb273b230584979a19.PNG' /> In the above case, PQ is called a non-intersecting line with respect to the circle . TRUE OR FALSE ?

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 :
<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 11 :
<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 12 :
<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 13 :
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 14 :
<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 15 :
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 16 :
<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 17 :
<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 18 :
<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 19 :
State true or false. Only two tangents can be drawn to a circle from an external point.

Question 20 :
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 21 :
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 22 :
<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 23 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?

Question 24 :
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 25 :
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