2. 9.Tangents and Secants to a circle
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9.Tangents and Secants to a circle
1. Secant: A line which intersects a circle in two distinct points is called a secant of
the circle.
2. Tangent: A tangent to a circle is a line that intersects the circle in exactly one
point.
3. A tangent to a circle is perpendicular to the radius through the point of contact.
4. A line drawn through the end point of a radius and perpendicular to its tangent
to the circle.
5. No tangent can be drawn to a circle from a point lying inside it.
6. One and only one tangent can be drawn to a circle at a point on the circle.
7. Two tangents can be drawn to a circle from a point lying outside it.
8. Length of the tangent: The length of the segment of the tangent between the
point and the given point of contact with the circle is called the length of the
tangent from the point to the circle.
9. The lengths of two tangents drawn from an external point to a circle are equal.
10. If two tangents are drawn to a circle from an external point, then
(i) They subtend equal angles at the center.
(ii)They are equally inclined to the segment, joining the center to that point.
11. For a circle of radius we have
(i) Circumference =
(ii) Area =
(iii) Area of semi-circle =
12. If and are the radii of two concentric circles such that then the area
enclosed by the two circles =
13. If a sector of a circle of radius r contains an angle of . Then
(i) Length of the arc of the sector =
(ii) Perimeter of the sector =
(iii) Area of the sector =
(iv) Area of the segment = (Area of the corresponding sector-
Area of the corresponding triangle)
3. 9.Tangents and Secants to a circle
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1) The length of tangent from a point 15cm away from the centre of a circle of
radius 9cm is________
(a)24 (b) (c) (d)None [ 3 ]
2) The Circumference of a circle is 100cm. The side of a square inscribed in the
circle is =_______cm
(a) (b) (c) (d)
3) The length of tangents drawn from an external point to a circle are
(a)different (b)
(c)perpemdicular (d)None [ 2 ]
4) If tangents PA and PB from a point to a circle with centre O are inclined to each
other at angle of then
(a) (b) (c) (d)
5) In the fig. LN is a diameter then
(b) (c) (d)
6) If a circle touches all the four sides of a quadrilateral ABCD. Then which of the
following is true
(a) (b)
(c) (d) [ 3
7) If PT is tangent drawn from a point P to a circle touching it at T and O is the
centre of the circle, then
(a) (b) (c) (d) [ 3 ]
8) The angles subtended by major arc at the centre is
(a) (b) (c) (d)
9) Number of tangents to a circle which are parallel to a secant are
(a)1 (b)2 (c)3 (d)None
10) From a point Q, the length of the tangent to a circle is 24cm and the distance of
Q from the centre is 25cm. Then the radius of the circle=______cm.
(a)7 (b)12 (c)15 (d)Non
4. 9.Tangents and Secants to a circle
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11) A circle can have _____ parallel tangents at the most
(a)3 (b) (c) (d) [
12) The angle between a tangent to a circle and the radius drawn at the point of
contact is
(a) (b) (c) (d) [ 4 ]
13) The concentric circles are of radii 12cm and 13cm are drawn. Then the length
of the chord of the larger circle which touches the smaller circle is ______cm.
(a) (b) (c) (d) 2
14) The area of a sector, whose radius is 6cm and the angle is =______
(a)28.28 (b)30.8 (c)51.33 (d)None [ 1 ]
15) The area of the designed region in the figure common between the two
quadrants of the circle of radius 10cm each take is = _______
(a)53 (b)57 (c)52 (d)none
16) A chord of a circle radius subtends an angle at the centre. Then
the area of the corresponding minor segment of the circle is =______
(a)225 (b)200 (c)150 (d) None
[ 3 ]
17) In the figure, BC =___cm ప్రక్క ప్టములో BC=_____సెం.మీ.
(a)1.4 (b)2.5 (c)1.5 (d)2.3
[ 2 ]
18) If the Perimeter of a sector of a circle of radius 6.5cm is 29cm
then its area is _______
(a) (b) (c) (d)
19) Two concentric circles are of radii 5cm and 3cm. Find the length of the chord
of the larger circle=________cm
(a)4 (b)16 (c)8 (d)6 [ 3 ]
20) If all the sides of a parallelogram touch a circle, then the parallelogram is
(a)Rectangle (b)Square
5. 9.Tangents and Secants to a circle
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(c)trapezium (d)Rhombus
21) Angle in a semi-circle is
(a) (b) (c) (d)
22) In the figure,
(a) (b) (c) (d)
23) Area of semi circle is
(a) (b) (c) (d)
24) In the figure ,
(a) (b) (c) (d)
25) Angle in a semi circle at the center is
(a) (b) (c) (d) None
26) In the figure, the largest chord is
(a) (b) (c) (d) GH
27) If a circle touches all the four sides of a quadrilateral ABCD points P, Q, R and S
then AB+CD=
(a) (b) (c) (d)
28) Cyclic Rhombus is a
(a)Parallelogram (b)Square (c)trapezium (d) None
29) The diameter of a circle is 10cm. It has a chord of length 8cm. Then the
distance of the chord from the center is _______cm
6. 9.Tangents and Secants to a circle
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(a) (b)7 (c) (d) 3
30) ABCD is cyclic quadrilateral, AD is a diameter and
, then
(a) (b) (c) (d)
31) In the figure
(a) (b)48cm (c) (d) 2cm
32) Two circles of radii x and y touch each other externally and ST is their
common tangent touching them at S and T, then
(a) (b)xy (c) (d)
33) In the figure
(a) (b) (c) (d)
34) The area of the shaded region in the fig. ABCD is a square of
side 7cm and APD and BPC are semicircles is __________
(a)100.5 (b)10.5 (c) (d) None
7. 9.Tangents and Secants to a circle
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35) A round table top has six equal designs as shown in the figure . If
the radius of the table tope is 14cm, the cost of making the designs with paint
at the rate of Rs. 5/- per is Rs._________
(a)534 (b)535 (c)536 (d) 570
36) The angle between a tangent to acircle and the radius drawn at the point of
contact is
(a) (b) (c) (d)
37) From a point Q, the length of the tangent to a circle is 24cm and the distance of
Q from the centre is 24cm. Then the radius of the circle is
(a) (b) (c) (d)
38) If AP and AQ are the two tangents to a circle with centre at O.
so that , then
(a) (b) (c) (d)
39) If tangents PA and PB from a point P to a circle with centre O are inclined to
each other at an angle Then
(a) (b) (c) (d)
40) In th fig r XY nd X’Y’ r two p r t ng nts
to a circle with center at O and another tangent AB with point of contact C
intersecting XY.
(a) (b) (c) (d)
41) A chord of a circle of radius 10cm. subtends a right angle at the centre. Then
the area of the minor segment
8. 9.Tangents and Secants to a circle
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(a) (b) (c) (d) None
42) A tangent PQ at a point P of a circle of radius 5cm meets a line through the
c ntr “O” t point Q s ch th t OQ cm th n th ngth of PQ is
(a) (b) (c) (d)
43) In the figure, RQ is the tangent to the circle with centre at
“O” If SQ cm nd QR cm th n OR
(a) (b) (c) (d)
44) At one end of a diameter PQ of a circle of radius 5cm, tangent XPY is drawn to
the circle. The length of chord AB is parallel to XY and at a distance of 8cm
from P is
(a) (b) (c) (d)
45) If PT is tangent drawn from a point P to a circle touching it at T and O is the
centre of the circle, then
(a) (b) (c) (d)
46) The area of a sector is one twelfth that of the complete circle. Then the angle
of that sector is
(a) (b) (c) (d)
47) A circular grassy plot of land, 42m in diameter has a path 3.5m wide running
round it on the outside. Then the cost of gravelling the path at Rs. 4/- per
square meter is
(a) (b) (c) (d)
48) AB and CD are respectively arcs of two concentric
circles of radii 21cm and 7cm at centre O. If the area of the
shaded region ________
(a) (b) (c) (d) None
49) A chord of a circle of radius 14cm makes a right angle at the centre. The area
of the major segments of the circle________
9. 9.Tangents and Secants to a circle
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(a) (b) (c) (d) 25.6
50) In a circle of radius 21cm, an arc subtends an angle of at the center. Then
the length of the area
(a) (b) (c) (d)
Answers
1 2 3 4 5 6 7 8 9 10
c c b a b c c c b a
11 12 13 14 15 16 17 18 19 20
c d b a b c b c c b
21 22 23 24 25 26 27 28 29 30
a b c d c b d d d b
31 32 33 34 35 36 37 38 39 40
b a a b a d a b a c
41 42 43 44 45 46 47 48 49 50
a d d d c a b b b a
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