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. While constructing a similar triangle, we need to construct _______ angle at any one of the bases of the given triangle. 
  • An obtuse angle
  • An acute angle
  • a right angle
  • a reflex angle
Submit

Solution :

While constructing a similar triangle, we need to construct an acute angle at any one of the bases of the given triangle. 
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Q2. In the figure below, if ∠XAO = 30°, then what is the measure of ∠XAY?  
  • 30°
  • 45°
  • 60°
  • 90°
Submit

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
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Q3. 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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Q4. 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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Q5. 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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Q6. If two tangents are drawn from a point to a circle, then this point should definitely lie 
  • inside the circle
  • outside the circle
  • on the circle
  • none of these
Submit

Solution :

From a point external to the circle, we can draw only two tangents to it.
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Q7. PQ is divided into 2 equal parts at A, then PA:AQ is 
  • 1:3
  • 1:1
  • 2:1
  • 1:2
Submit

Solution :

P-A-C, PA = x, AQ = x 
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Q8. The scale factor of ∆PQR, which is similar to ∆TUV, such that PR:TV = 6:2 is
  • 8
  • 6
  • 3
  • 2
Construction of Similar Triangles

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Submit

Solution :

The scale factor of ∆PQR, which is similar to ∆TUV, such that PR:TV = 6:2 is 3 .
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Q9. The centre of a circle can be found from a point of intersection of 
  • two diameters
  • two radii
  • the perpendicular of two chords
  • the perpendicular bisectors of two chords
Submit

Solution :

The centre of a circle can be found from a point of intersection of the perpendicular bisectors of two chords. 
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Q10. The number of tangents which can be drawn from a point inside a circle to it is
  • 0
  • 1
  • 2
  • 3
Submit

Solution :

No tangents can be drawn from a point inside a circle.
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Q11. 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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Q12.   In the figure above, if the angle between the tangents is 70o, then the angles between the two radii will be
  • 110o
  • 125o
  • 130o
  • 135o
Submit

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.
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Q13. 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
Submit

Solution :

A-P-R-B If PB = 2x, BA = 3x, AP = x, PR = RB = x.
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Q14. 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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Q15. We can draw only one tangent to a circle from a point
  • inside the circle
  • outside the circle
  • on the circle
  • none of these
Submit

Solution :

We can draw only one tangent to a circle from a point on the circle.
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Q16. A tangent cuts the circle at 
  • one point
  • two points
  • no point
  • three points
Submit

Solution :

A tangent cuts the circle at one point. 
Still have doubt? Watch Video
Q17. 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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Submit

Solution :

While constructing ∆PQR similar to ∆ABC such that AB:PQ = 3:5, the larger triangle is DPQR.
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Q18.   If the angle between the tangents is 50° (as shown in the figure), then the angles between the two radii will be 
  • 120°
  • 125°
  • 130°
  • 135°
Submit

Solution :

In ∆AXO,  ∠XAO = 25° then ∠XOA = 180° − 90° − 25° = 65° ∠XOY = 130° 
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Q19. 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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Q20. The number of tangents which can be drawn from a point outside a circle to it is 
  • 0
  • 1
  • 2
  • 3
Submit

Solution :

The number of tangents which can be drawn from a point outside a circle to it is 2.
Still have doubt? Watch Video
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