Question 1 :
<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 2 :
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 3 :
Is it TRUE or FALSE, that If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ?

Question 5 :
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 6 :
A line and a circle in the same plane can co-exist in _______ different ways.

Question 7 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a49273b230584979914.PNG' /> In the above figure, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to

Question 8 :
A tangent to a circle intersects it in how many point(s)?

Question 9 :
If a hexagon ABCDEF circumscribe a circle, is it TRUE or FALSE that AB + CD + EF = BC + DE + FA?

Question 10 :
<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 11 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbd273b230584979a06.png' /> The area of an equilateral triangle ABC is 17320.5 $cm^{2}$ . With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see the above image). Find the area of the shaded region. (Use $\pi$= 3.14 and $\sqrt{3}$ = 1.73205)

Question 12 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bab273b2305849799ef.png' /> Find the area of the shaded region in the above figure, where ABCD is a square of side 14 cm.

Question 13 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3c273b23058497995d.jpg' /> In the above figure, ABCD is a trapezium with $AB\ \parallel\ DC$, AB = 18 cm, DC = 32 cm and distance between AB and DC is 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region.

Question 14 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bb7273b2305849799ff.png' /> (As shown in the above image)From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut . Find the area of the remaining portion of the square.

Question 15 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a46273b230584979910.jpeg' /> The above figure depicts an archery target marked with its five scoring regions from centre outwards as gold, red, blue, black and white. The diameter of the region representing gold score is 21 cm and each of the ofher bands is 10.5 cm wide. Find the area of blue scoring region.

Question 16 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b3d273b23058497995e.jpg' /> In the above figure, a floor of a room of dimensions $5\ m\times4\ m$ covered with circular tiles of diameters 50 cm each is shown. Find the area of the floor that remains uncovered with tiles.

Question 17 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bbb273b230584979a04.png' /> The above figure depicts a racing track whose left and right ends are semicircular.The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide , find the area of the track.

Question 18 :
Find the area of a sector of a circle of radius 21 cm and central angle $120^{\circ}$ .

Question 19 :
If Q $\left(0, 1\right)$ is equidistant from P $\left(5, –3\right)$ and R $\left(x, 6\right)$, find the values of x.

Question 20 :
Determine, if the points (1,5), (2,3) and (-2 ,-11) are collinear.

Question 21 :
Find the coordinates of the point which divides the line segment joining the points $\left(4, – 3\right)$ and $\left(8, 5\right)$ in the ratio 3 : 1 internally.

Question 22 :
The vertices of a ∆ABC are A $\left(4, 6\right)$, B$\left(1, 5\right)$ and C $\left(7, 2\right)$. A line is drawn to intersect sides AB and AC at D and E respectively, such that $\frac{AD}{AB}$=$\frac{AE}{AC}$=$\frac{1}{4}$. Calculate the area of triangle ABC.

Question 23 :
∆ ABC with vertices A (–2, 0), B (2, 0) and C (0, 2) is similar to ∆ DEF with vertices D (–4, 0) E (4, 0) and F (0, 4). State true or false.

Question 24 :
Find the distance between the following pair of points: (-5,7) , (-1,3).

Question 25 :
Let A $\left(4, 2\right)$ , B $\left(6, 5\right)$ and C $\left(1, 4\right)$ be the vertices of ∆ABC.The median of A meets BC at D. Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1

Question 26 :
The line segment joining the points A (3, 2) and B (5,1) is divided at the point P in the ratio 1: 2 and it lies on the line 3x – 18y + k = 0. Find the value of k.

Question 27 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bd7273b230584979a29.png ' /> The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the above image. The students are to sow seeds of flowering plants on the remaining area of the plot.What will be the area of ∆PQR if C is the Origin?

Question 28 :
Find the distance between the points $\left(0, 0\right)$ and $\left(36, 15\right)$.