# Full fledge assessment videos for constructions

Full fledge assessment (Please watch the above videos before attempting this assessment)

Question 1 of 20
Q1. To divide a line segment in 5:3, we have to make
• 5 equal divisions
• 3 equal divisions
• 2 equal divisions
• 8 equal divisions

### Solution :

To divide a line segment in m:n, we have to make m+n equal divisions.
Q2. Two tangents drawn from the external points to a circle are
• Perpendicular
• Parallel
• Equal
• None of these

### Solution :

Two tangents drawn from the external points to a circle are equal.
Q3. To divide a line segment in m:n, we have to make
• M equal divisions
• N equal divisions
• m+n equal divisions
• m-n equal divisions

### Solution :

To divide a line segment in m:n, we have m+n equal divisions.
Q4. The tangent is perpendicular to the
• Diameter
• None of these

### Solution :

The tangent makes an angle of measure 90o with the radius and diameter.
Q5. In the figure below, ∠XAO = 30°. What is the measure of ∠XOA? • 30°
• 45°
• 60°
• 90°

### Solution :

∠XAO = 30° ∠OXA = 90° So, ∠XOA = 60° … (sum of the angles of a triangle)
Q6. If AB is divided into 3 equal parts at P and R, then
• AP = 1/3 AB
• PB = 2/3 BA
• PR = RB
• All of these

### Solution :

A-P-R-B If PB = 2x, BA = 3x, AP = x, PR = RB = x.
Q7. The length of the tangent from the external point P is 15 cm, and the distance of P from the centre is 17 cm. So, the radius of the circle is
• 6 cm
• 7 cm
• 8 cm
• 9 cm

### Solution :

Q8. In the figure below, if AO = 29 cm, XO = 21 cm, then AY =? • 25 cm
• 24 cm
• 22 cm
• 20 cm

### Solution :

Since the tangent is perpendicular to the radius, By Pythagoras' theorem, 292 = 212 + AX2 AX2 = 400 AY = AX = 20 cm
Q9. How many tangents can be drawn to a circle having a diameter 15 cm from a point at a distance of 7.5 cm from the centre?
• 0
• 1
• 2
• 3

### Solution :

The distance from the centre is 7.5 cm. The radius is 7.5 cm. Since the point lies on the circle, 1 tangent can be drawn to the circle.
Q10. If the scale factor is less than one, then the new triangle is
• larger than the original one
• smaller than the original one
• equal to the original one
• None of these
Construction of Similar Triangles

" >

### Solution :

If the scale factor is less than one, then the new triangle is smaller than the original one.
Q11. In the figure below, if ∠XAO = 30°, then what is the measure of ∠XAY? • 30°
• 45°
• 60°
• 90°

### Solution :

The line joining the centre of a circle to the external point bisects the angle between two tangents and two radii.  2∠XAO = ∠XAY
Q12. The angle drawn in a semicircle from the end points of the diameter is
• 30°
• 45°
• 60°
• 90°

### Solution :

The angle drawn in a semicircle from the end points of the diameter is 90°.
Q13. The number of tangents which can be drawn through a point on the circle is
• one
• two
• three
• many

### Solution :

Only one tangent can be drawn through a point on the circle.
Q14. 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
• 7 equal divisions
• 6 equal divisions
• 5 equal divisions
• 2 equal divisions

### 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)).
Q15. If PQ is divided into 5 equal parts at A, B, C and D, then PB:BQ is
• 2:3
• 3:2
• 2:5
• 5:2

### Solution :

P-A-B-C-D-Q, PB = 2x, BQ = 3x
Q16. While constructing ∆PQR similar to ∆ABC such that AB:PQ = 3:5, we need to make an acute angle at A and divide it
• 3 times
• 5 times
• 8 times
• 10 times
Construction of Similar Triangles

" >

### Solution :

While constructing a triangle similar to the given triangle, such that their sides are in the ratio m:n, we need to make an acute angle and divide it max (m,n) times.
Q17. A tangent cuts the circle at
• one point
• two points
• no point
• three points

### Solution :

A tangent cuts the circle at one point.
Q18. How many tangents can be drawn to a circle having a diameter 12 cm from a point at a distance of 10 cm from the centre?
• 0
• 1
• 2
• 3

### Solution :

The distance from the centre is 10 cm. The radius is 6 cm. Since the point lies outside the circle, 2 tangents can be drawn to the circle.
Q19. The number of tangents which can be drawn from a point inside a circle to it is
• 0
• 1
• 2
• 3

### Solution :

No tangents can be drawn from a point inside a circle.
Q20. In the figure below, AO = 5 cm and XO = 3 cm, then AX =? • 4 cm
• 5 cm
• 6 cm
• 7 cm

### Solution :

As the radius is perpendicular to the tangent,  By Pythagoras' theorem, 52 = 32 + AX2AX2 = 16 AX = 4

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