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

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

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°

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

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

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

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

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

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

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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

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

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

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°

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

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

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

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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

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°

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

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

Solution :

To divide a line segment in 4 equal parts, we need to draw a perpendicular bisector three times.
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