October 29, 2020
9.TANGENTS AND SECANTS TO A CIRCLE
Hi friends and my dear students! In this post, I have covered Important questions for 10th class maths chapter-8 Similar triangles, Chapter wise previous year Questions. After Reading Please do share it with your friends. Learn maths for All classes here
PRIORITY-I
1 MARK QUESTIONS:
1.
Define a tangent and a secant to a circle
2.
Find the length of a tangent to a circle with centre O and radius 6cm from a
point such that OP = 10cm?
3.
Draw a circle and two lines parallel to given line such that one is a tangent
and the other a secant to the circle?
4.
Calculate the length of a tangent from a point 15cm away from the centre of
circle of radius 9cm?
5.
Find the area of sector whose radius is 7cm, with the given angle 600?
6.
The length of the minute hand of a clock is 14cm. Find the area of swept by
minute hand in 10minutes?
2 MARKS QUESTIONS
7.
Prove that the tangent at any point of a circle is perpendicular to radius
through the point of contact?
8.
A tangent PQ at a point P of a circle of radius 5cm meets a line through the
centre O at a point Q so that OQ= 12cm. find the length of PQ?
9.
Prove that the tangents to a circle at the end points of a diameter are
parallel?
10. Prove that the lengths of
tangents drawn from an external point to a circle are equal?
11.
If a circle touches all four sides of a quadrilateral ABCD at points PQRS, then
prove that AB+CD= BC+DA?
12.
Two concentric circles are radii 5cm, 3cm are
drawn. Find the length of the chord of the larger circle which touches the
smaller circle?
13.
Prove that the parallelogram circumscribing a circle is a rhombus?
14.
A chord of circle of a radius 10cm subtends a right angle at the centre. Find
the area of the corresponding minor segment and major segment?
15. A chord of circle of a radius 12cm subtends an angle of 1200 at the centre. Find the area of the corresponding minor segment of the circle?
4 MARKS QUESTIONS
16.
Draw a pair of tangents to a circle of radius 5cm which are inclined to each
other at an angle 600?
17.
Draw a circle of radius 6cm. from a point 10cm away from its centre, construct
the pair of tangents to the circle and measure their lengths. Verify by using
Pythagoras theorem?
18.
Construct a tangent to a circle 4cm from a point on the concentric circle of
radius 6cm and measure its length. Also verify the measurement by actual
calculation?
19. Draw a circle with the help
of a bangle. Take a point outside the circle construct the pair of tangents
from this point to the circle measure them write conclusion.
20. Find the area of the
segment AYB showing in the adjacent figure. If radius of the circle is 21 cm
and AOB = 1200?
21. Find the area of the
segments shaded in figure, if PQ = 24 CM., PR = 7 CM. and QR is
the diameter of the circle with centre O (Take π=22/7)?
Also Check
Important questions for 10th class maths chapter-1 Real numbers
Important questions for 10th class maths chapter-4 LINEAR EQUATIONS
Important questions for 10th class maths chapter-3 polynomial
Important questions for 10th class Maths chapter-5 Quadratic equations
Important questions for 10th class Maths chapter-10 Mensuration,
Important questions for 10th class Maths chapter-6 Progression
Important questions for 10th class Maths chapter-7 Coordinate Geometry
PRIORITY II:
MARK QUESTIONS:
1.
ON SIDE 3 AB as diameter of right angled triangle ABC is a circle is drawn
intersecting hypotenuse AC in p prove PB=PC
2.
Write the formulae for segment area in a circle radius ‘r’ given that the sector
angle is ‘𝜽’
3.
What is the angle subtended is a circle is centre radius 6cm by an arc of
length 3πcm
4.
Find the length of tangent drawn from a point 8cm away flows the center of a
circle of radius 6cm
5. How many parallel tangents
can a circle have?
6.
Two concentric circles have center at ‘o’ OP=4cm an OB=5cm AB is a chord of
outer circle and a tangent to inner circle at p find length of p
7.
AP and AQ are two tangents of a circle with center ‘o’ and ∟Q= 450
then find ∟POQ
8.
What can you say about the tangents drawn at ends of diameter of a circle?
9.
Draw rough sketch of tangent drawn from external point
10.
The circumference of a circle exceeds the diameter by 16.8cm find the
circumference of the circle
11.
What is the difference between a tangent and secant
12.
Write the formula for the area of a sector and explain the variables used in
the formula
13.
How can you mark the centre of a circle if the centre of a circle is unknown?
14.
How can you find the area of major circle segment using area of minor circle
segment?
15.
The tangents to a circle at the end points of diameter are parallel represent
the statement diagrammatically
16.
Define the segment of a circle? Draw different types of segments of a circle?
17. A point is 13cm away from
the center of the circle the length of the tangent drawn from A to the circle
is 12cm find the radius of the circle
2 MARKS QUESTAIONS:
1.
AB and AC are two tangents to a
circle with centre ‘o’ . if∟OAB OAB =x then find the value of ‘x’ OAB
2.
If area of a regular hexagon is 24√3 sq.cm find
its side
3.
Find area of quadrant of circle whose
radius is 7cm
4.
A chord AB of 8cm is drawn is a
circle with centre ‘o’ of radius 5cm find the length of tangents from external
point p to A and B
5.
The length of tangent to a circle of
radius 2.5cm from an external point ‘p’ is 6cm find distance of p from nearest
point to a circle
6.
The area of circle is 220cm2 then
find area of square inscribed in it
7.
If radius of two concentric circles
is 8cm and 10cm then find length of chord of larger circle which is tangent to
other
8.
A sector is cut from a circle of
radius 7cm if the angle of sector is 720 find area
9. If two tangents to a circle of radius 5cm are
inscribed to each other at angle of 600 then find the length of each
tangents
4
MARKS QUESTIONS:
1.
A car has two wipers which do not overlap. Each wiper has a blade of length 25
cm. sweeping through an angle of 115°. Find the total area cleaned at each
sweep of the blades.?
2. Find the area of the shaded
region in figure, where ABCD is a square of side 10cm. and semicircles are
drawn with each side of the square as diameter (use π = 3.14)
3. Find the area of the shaded
region in figure, if ABCD is a square of side 7cm. and APD and BPC are
semicircles.
4.
AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7
cm with centre O. If ∟AOB =300 then find the area of the shaded
region(use = π=22/7)
5.
A round table top has six equal designs, if the radius of the table top is 14cm
then find the cost of making the designs with paint at the rate of 5/- per cm2
6. Calculate
the area of the designed region, common between the two quadrants of the
circles of radius 10cm each
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