Q1.
If the angle between the tangents
is 50
o (as shown in the figure), then the angles between the two
radii will be
Solution :
In ∆AXO,
∠XAO = 25°
then ∠XOA = 180° − 90° − 25° = 65° ∠XOY = 130°
Q2. A tangent and radius of the circle
make an angle of measure
Solution :
A
tangent and radius of the circle make an angle of measure 90°.
Q3. If the length of the tangent from
the external point P is 12 cm, and the distance of P from the centre is 13 cm, then the radius of the circle is
Solution :
By Pythagoras' theorem,
132
= 122 + radius2
radius2
= 25
radius
= 5 cm
Q4. While
constructing ∆XYZ similar to ∆STU such that SU:XZ = 6:7, the smaller triangle is
Construction of Similar Triangles" >
Solution :
While
constructing ∆XYZ similar to ∆STU such that SU:XZ = 6:7, the
smaller triangle is DSTU.
Q5. If PQ is divided into 3 equal
parts at A and B, then PB:BQ is
Solution :
P-A-B-Q
If
PA = x, PB = 2x, BQ = x.
Q6.
In the
figure above, if the angle between the tangents is 70
o, then the
angles between the two radii will be
Solution :
In ∆AXO,
∠XAO = 35°
then ∠XOA = 180°− 90° − 35° = 55°
∠XOY = 110° … The line joining the centre of a circle and an
external point bisects the angle between the tangents and the radius.
Q7. While
constructing ∆ABC similar to ∆TUV such that AB:TU = 1:5, the scale factor is
Construction of Similar Triangles" >
Solution :
While
constructing ∆ABC similar to ∆TUV such that AB:TU = 1:5, the
scale factor is 1/5.
Q8. If PQ is
divided into 5 equal parts at A, B, C and D, then PB:BQ is
Solution :
P-A-B-C-D-Q,
PB = 2x, BQ = 3x
Q9. The
number of tangents which can be drawn from a point inside a circle to it is
Solution :
No
tangents can be drawn from a point inside a circle.
Q10. While
constructing a similar triangle such that its corresponding sides are in the
ratio 5:2, we need to construct an acute angle at any one of the bases of the
given triangle and make
Solution :
While
constructing a similar triangle, we need to construct an acute angle at any
one of bases of the given triangle and make 5 equal divisions (max (5 and
2)).
Q11. The angle drawn in a semicircle
from the end points of the diameter is
Solution :
The
angle drawn in a semicircle from the end points of the diameter is 90°.
Q12. If AB is divided into 3 equal parts at P
and R, then PB =?
Solution :
A-P-R-B
If PB =
2x, then BA = 3x.
Q13. PQ is
divided into 2 equal parts at A, then PA:AQ is
Solution :
P-A-C,
PA = x, AQ = x
Q14. A tangent cuts the circle at
Solution :
A
tangent cuts the circle at one point.
Q15. If two
lines meet a transversal and they make equal corresponding angles, then the
two lines are
Solution :
If two lines meet a transversal and they
make equal corresponding angles, then the two lines are parallel.
Q16. To divide a line segment in 5:3, we
have to make
Solution :
To
divide a line segment in m:n,
we have to make m+n equal divisions.
Q17. The
number of tangents which can be drawn through a point on the circle is
Solution :
Only one
tangent can be drawn through a point on the circle.
Q18. If AB is divided into 4 equal
parts at P, Q and R, then PQ =?
Solution :
A-P-Q-R-B
If PQ = x, BA = 4x.
Q19. To
divide a line segment in 4 equal parts, we need to draw
Solution :
To
divide a line segment in 4 equal parts, we need to draw a perpendicular
bisector three times.
Q20. The centre of a circle lies on the
Solution :
The centre of a circle lies on the perpendicular bisector of its
chord.
