Download Date:10/01/2015 UNIT TEST Marks:55

ADARSH VIDYALAYA(RMSA) BIBBALLI
TQ-SEDAM, DIST-KALBURGI
10th STD
Time: 50 Min
SUBJECT: MATHEMATICS
DATE:10/01/2015
UNIT TEST
MARKS:55
II. Answer the following
1x7=7
1) Two circles of radii 4cm and 3 cm touch each other externally. Find the distance
between their centers.
2) What are the angles in the Major segment?
3) What is the name of a straight line which intersects a circle at two distinct points?
4) The two circles are intersection, what is the maximum number of common tangents
to be drawn?
5) What is the distance between the circles of radius R and r touch each other internally.
6) How many transverse tangents to be drawn for two circles touch each other
externally?
7) What are concentric circles?
II. Answer the following
2 x 8 = 16
8. Draw a circle of diameter 6 cm and construct two tangents at the ends of the radii
such that the angle between the radii is 110°.
9. Draw a circle of radius 4 cm and construct a pair of tangents such that angle
between them is 50°.
10. Construct a pair of tangents to a circle of radius 3.5 cm from a point 3.5 cm away
from the circle. Measure the length of the tangent.
11) Construct a pair of tangents to a circle of radii 5 cm, and the angle between them is
400
12) In a circle of radius 3.5cm draw two radii such that the angle between them is700
Construct tangents at the non-centre ends of the radii.
13) In a circle of radius 3cm draw two radii such that the angle between them is600
Construct tangents at the non-centre ends of the radii.
14) Construct a pair of tangents to a circle of radius 3cm from a point 7cm away from the
centre.
15) In a circle of radius 4.5cm draw two radii such that the angle between them is700
Construct tangents at the non-centre ends of the radii.
II. Answer the following
3 x 4 = 12
16. If two circles touch each other, prove that their centres and their point of contact
are collinear.
17. If two circles touch each other internally their centres and the point of contact are
collinear. Prove.
18. A straight drawn through the point of contact of two circles with centres A and B
intersect the circles at P and Q respectively. Show that AP and BQ are parallel.
20) Prove that the tangents drawn from an external point to a circle
(a) Are equal
( b) Subtend equal angles at the centre
(c) Are equal inclined to the line joining the centre and the external point.
II. Answer the following
4 x 5 = 20
21. Draw two circles of radii 4.5 cm and 2 cm at a distance of 11 cm apart from their
centres. Construct direct common tangents to them and measure their length.
22. Construct a transverse common tangent to two circles of radii 4 cm and 2 cm
having their centre 10 cm apart. Measure the length of the TCT and verify by
calculation.
23. Construct a transverse common tangent to two circles of radii 3 cm and 2 cm with
their centres 9 cm apart. Measure the length of the tangent and verify.
24. Construct two direct common tangents to two circles of radii 5 cm and 2.5 cm
whose centres are 11 cm apart. Measure its length.
25) Draw transverse common tangents to two circles of radii 5cm and 2cm having
Their centers 9cm apart and measure their lengths.