Full fledge assessment videos for constructions

Understand to construct how to divide a line segment in a given ratio. Con...

This video explains the construction of tangents to a given circle from a p...

Understand to construct how to divide a line segment in a given ratio. Con...

Construction of tangents to a given circle from a point on the circle and f...

Understand to construct how to divide a line segment in a given ratio. Con...

Construction of tangents to a given circle from a point on the circle and ...

This video covers an application on similar triangles

This video covers an application on tangents from external point

This video covers an application based on construction related to section f...

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

Question 1 of 20
Q1. When parallel lines meet a transversal, they make equal 
  • alternate angles
  • interior angles
  • exterior angles
  • None of these
Submit

Solution :

When parallel lines meet a transversal, they make equal alternate angles. 
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Q2. 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
Submit

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.
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Q3. A tangent and radius of the circle make an angle of measure 
  • 45°
  • 90°
  • 180°
  • 270°
Submit

Solution :

A tangent and radius of the circle make an angle of measure 90°.
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Q4. In the figure below, if AO = 29 cm, XO = 21 cm, then AY =?  
  • 25 cm
  • 24 cm
  • 22 cm
  • 20 cm
Submit

Solution :

Since the tangent is perpendicular to the radius, By Pythagoras' theorem, 292 = 212 + AX2 AX2 = 400 AY = AX = 20 cm 
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Q5. 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 
  • 5 cm
  • 6 cm
  • 7 cm
  • 8 cm
Submit

Solution :

By Pythagoras' theorem,  132 = 122 + radius2 radius2 = 25 radius = 5 cm
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Q6. If AB is divided into 3 equal parts at P and R, then PB =?
  • 1/4 AR
  • 1/2 BA
  • 1/4 AB
  • 2/3 AB
Submit

Solution :

A-P-R-B If PB = 2x, then BA = 3x.
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Q7. To divide a line segment in 5:3, we have to make
  • 5 equal divisions
  • 3 equal divisions
  • 2 equal divisions
  • 8 equal divisions
Submit

Solution :

To divide a line segment in m:n, we have to make m+n equal divisions.
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Q8. 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
Submit

Solution :

To divide a line segment in m:n, we have m+n equal divisions.
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Q9. While constructing ∆PQR similar to ∆ABC such that AB:PQ = 3:5, the larger triangle is 
  • ∆ABC
  • ∆PQR
  • Both are equal
  • None of these
Construction of Similar Triangles

" >
Submit

Solution :

While constructing ∆PQR similar to ∆ABC such that AB:PQ = 3:5, the larger triangle is DPQR.
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Q10. A tangent cuts the circle at 
  • one point
  • two points
  • no point
  • three points
Submit

Solution :

A tangent cuts the circle at one point. 
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Q11. In the figure below, AO = 5 cm and XO = 3 cm, then AX =?  
  • 4 cm
  • 5 cm
  • 6 cm
  • 7 cm
Submit

Solution :

As the radius is perpendicular to the tangent,  By Pythagoras' theorem, 52 = 32 + AX2AX2 = 16 AX = 4
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Q12. Two tangents drawn from the external points to a circle are 
  • Perpendicular
  • Parallel
  • Equal
  • None of these
Submit

Solution :

Two tangents drawn from the external points to a circle are equal. 
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Q13. The angle drawn in a semicircle from the end points of the diameter is 
  • 30°
  • 45°
  • 60°
  • 90°
Submit

Solution :

The angle drawn in a semicircle from the end points of the diameter is 90°. 
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Q14. The centre of a circle lies on the
  • Perpendicular
  • perpendicular bisector
  • perpendicular of its chord
  • perpendicular bisector of its chord
Submit

Solution :

The centre of a circle lies on the perpendicular bisector of its chord.
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Q15. 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
Submit

Solution :

By Pythagoras' theorem, 172 = 152 + radius2 radius2 = 64 radius = 8 cm
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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

" >
Submit

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. 
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Q17. To construct a line parallel to the given line, we use 
  • The alternate angles property
  • The corresponding angles property
  • Both A and B
  • None of these
Submit

Solution :

To construct a line parallel to the given line, we use the corresponding angles and alternate angles property. 
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Q18. In the figure below, ∠XAO = 30°. What is the measure of ∠XOA?   
  • 30°
  • 45°
  • 60°
  • 90°
Submit

Solution :

∠XAO = 30° ∠OXA = 90° So, ∠XOA = 60° … (sum of the angles of a triangle) 
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Q19. The length of the tangent from the external point P is 40 cm and the distance of P from the centre is 41 cm, so the radius of the circle is 
  • 5 cm
  • 7 cm
  • 8 cm
  • 9 cm
Submit

Solution :

By Pythagoras' theorem, 412 = 402 + radius2 radius2 = 81 radius = 9 cm
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Q20. To divide a line segment in 4 equal parts, we need to draw 
  • perpendicular bisector two times
  • perpendicular bisector three times
  • perpendicular bisector four times
  • none of these
Submit

Solution :

To divide a line segment in 4 equal parts, we need to draw a perpendicular bisector three times.
Still have doubt? Watch Video
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