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

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°

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

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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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Q4. 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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Q5. 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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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

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

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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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

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

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°

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

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

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

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

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

Solution :

A tangent cuts the circle at one point. 
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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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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°

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

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

Solution :

The number of tangents which can be drawn from a point outside a circle to it is 2.
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