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All questions of Further Graphs & Tangents for Class 10 Exam
If TP and TQ are two tangents to a circle with centre O so that angle POQ = 110° then angle PTQ is equal to
- a)600
- b)800
- c)700
- d)900
Correct answer is option 'C'. Can you explain this answer?
If TP and TQ are two tangents to a circle with centre O so that angle POQ = 110° then angle PTQ is equal to
a)
600
b)
800
c)
700
d)
900
|
Krishna Iyer answered |
We know that the sum of angle made by two tangents joined by an exterior point and the angle made at the centre of the circle is equal to 180 degrees
So, Angle POQ + Angle PTQ = 180
110 + Angle PTQ = 180
Angle PTQ = 180- 110 = 70 degrees
So, Angle POQ + Angle PTQ = 180
110 + Angle PTQ = 180
Angle PTQ = 180- 110 = 70 degrees
Length of the tangent to a circle from a point 26 cm away from the centre is 24 cm. What is the radius of the circle?- a)11cm
- b)13 cm
- c)10 cm
- d)12cm
Correct answer is option 'C'. Can you explain this answer?
Length of the tangent to a circle from a point 26 cm away from the centre is 24 cm. What is the radius of the circle?
a)
11cm
b)
13 cm
c)
10 cm
d)
12cm
|
Kashish Juneja answered |
Length of tangent = 24 cmLength from the point to the centre of circle = 26 cm.
Join the point of contact and the centre of the circle.
We know that line drawn from centre to the tangent is always perpendicular.
So by using Pythagoras Theorem,
(26)^2 = (24)^2 + Square of other side.
(Other side)^2 = 676 - 576.
Other side = √100.
Other side = 10 cm
In which of the following is AD not the bisector of angle A?
- a)AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
- b)AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm
- c)AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm
- d)AB = 8 cm, AC = 24 cm, BD = 6 cm and CD = 24 cm
Correct answer is option 'C'. Can you explain this answer?
In which of the following is AD not the bisector of angle A?
a)
AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
b)
AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm
c)
AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm
d)
AB = 8 cm, AC = 24 cm, BD = 6 cm and CD = 24 cm
|
Amit Sharma answered |
The angle bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.So in this question,
So , Substituting the values of option C
LHS=5/1.5=1/0.5
RHS=10/3.5=2/0.7
So, RHS ≠ LHS
So , Substituting the values of option C
LHS=5/1.5=1/0.5
RHS=10/3.5=2/0.7
So, RHS ≠ LHS
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at the end points to those two radii of the side, the angle between which is- a)90°
- b)30°
- c)120°
- d)45°
Correct answer is option 'C'. Can you explain this answer?
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at the end points to those two radii of the side, the angle between which is
a)
90°
b)
30°
c)
120°
d)
45°
|
Vikram Kapoor answered |
∠OQP=90o=∠ORP since the angle, between a tangent to a circle and the radius of the same circle passing through the point of contact, is 90o.
∴ By angle sum property of quadrilaterals, we get ∠OQP+∠RPQ+∠ORP+∠ROQ=360o⟹90o+60o+90o+∠ROQ=360o⟹∠ROQ=120o.
A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?- a)1
- b)3
- c)Infinite
- d)2
Correct answer is option 'D'. Can you explain this answer?
A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?
a)
1
b)
3
c)
Infinite
d)
2
|
|
Anita Menon answered |
Two tangents can be drawn to a circle from a point outside the circle.
No tangent line can be drawn through a point within a circle, since any such line must be a secant line.
No tangent line can be drawn through a point within a circle, since any such line must be a secant line.
A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?- a)2
- b)1
- c)Infinite
- d)0
Correct answer is option 'A'. Can you explain this answer?
A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?
a)
2
b)
1
c)
Infinite
d)
0
|
|
Ananya Das answered |
Only two tangents can be drawn from an external point.No tangent can be drawn which touches points inside the circle.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 45° it is required to draw tangents at the end point of those two radii of the circle, the angle between which is :- a)105°
- b)135°
- c)145°
- d)70°
Correct answer is option 'B'. Can you explain this answer?
To draw a pair of tangents to a circle which are inclined to each other at an angle of 45° it is required to draw tangents at the end point of those two radii of the circle, the angle between which is :
a)
105°
b)
135°
c)
145°
d)
70°
|
Kajal Mehta Mehta answered |
135 degrees
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