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Quantitative Aptitude

MENSURATION MCQs

Regular Polygons, Triangles, Circles

Total Questions : 254 | Page 3 of 26 pages
Question 21. The statement "Length of chord is always greater than radius" is
  1.    True
  2.    False
  3.    Circle
  4.    Circumference
 Discuss Question
Answer: Option B. -> False
:
B
The length of the chord need not always be greater than the radius. Consider the figure, OP is the radius, AB is the chord.
OP = 5 cm, AB = 2 cm
The Statement
Question 22. Which of the following represent the diameters of the circle with center O?
Which Of The Following Represent The Diameters Of The Circle...
  1.    OP, OB
  2.    OQ, AB
  3.    OB, PQ
  4.    AB, PQ
 Discuss Question
Answer: Option D. -> AB, PQ
:
D
The diameter of a circle is a line segment which passes through the center of the circle and whose endpoints lie on the circle.
AB and PQ are the diameters of the circle.
Question 23. Which of the following is not a radius of the circle with center O?
Which Of The Following Is Not A Radius Of The Circle With Ce...
  1.    OA
  2.    AB
  3.    OC
  4.    OD
 Discuss Question
Answer: Option B. -> AB
:
B
The radius of a circle is a line segment connecting the center of the circle to any point on the circumferenceof the circle.
So, OA, OC, OD and OB are the radii of the given circle.
However, AB is the diameter.
Question 24. A circle with center O is shown. AB in the figure is a :
A Circle With Center O Is Shown. AB in The Figure Is A :
  1.    Diameter
  2.    Radius
  3.    Chord
  4.    Tangent
 Discuss Question
Answer: Option C. -> Chord
:
C
A chord of a circle is a line segment whose endpoints lie on the circle.
The diameter of a circle is the chord which passes through the center of the circle.
The line segment AB is a chord as it does not pass through the center of the circle.
Question 25. What will be the diameter of a circle of radius 18 cm?
  1.    36 cm
  2.    18 cm
  3.    9 cm
  4.    39 cm
 Discuss Question
Answer: Option A. -> 36 cm
:
A
Given that
The radius of thecircle = 18 cm
The diameter of thecircle = radius × 2
On substituting the values we get:
The diameter of the circle = 18 × 2 = 36 cm
Question 26. Which is the correct relation of radius and diameter?
  1.    r = 2D
  2.    D = 2r
  3.    r = D
  4.    r = 3D
 Discuss Question
Answer: Option B. -> D = 2r
:
B
Diameter = 2 × radius (or) twice the radius
D = 2r is the correct relation between them.
Question 27. A circle with center O is shown below. The line segment OA is the ____ of the circle.
A Circle With Center O Is Shown Below. The Line Segment OA ...
  1.    diameter
  2.    radius
  3.    chord
  4.    segment
 Discuss Question
Answer: Option B. -> radius
:
B
The radius of a circle is a line segment joining the center of the circle to any point on the circumferenceof the circle.
The line segment OA is the radius of the circle.
Question 28. ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. ADP = BEQ = 100. What is value of PRD?
ABC Is An Isosceles Triangle And AC, BC Are The Tangents At ...
 
  1.    60∘
  2.    50∘
  3.    20∘
  4.    Can't be determined 
 Discuss Question
Answer: Option C. -> 20∘
:
C
ADB is a straight line. Bylinear pair axiom,
ADP + PDB =180
100 + PDB =180
PDB =80
Similarly QED =80
We have, ∠DPE = 90(angle subtended by a diameter)
In DPE,
DPE + PED + EDP = 180
[Angle sum property of a triangle]
∠PED = 10
Similarly QDE =10
In DRE,
DRE + RDE + RED = 180
[Angle sum property of a triangle]
∠DRE = 160
PRE is a straight line.Bylinear pair axiom,
PRD + DRE =180
PRD + 160 =180
PRD =20
Question 29.  The length of the tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre is = ___ cm.
 Discuss Question

:
 The Length Of The Tangent Drawn To A Circle With Radius 7 ...
ABO= 90(point of contact)
Using Pythagoras theorem
AO2= AB2+ BO2
252= AB2+ 72
252- 72= AB2
24= AB
length of the tangent = 24 cm
Question 30. If AB is the tangent to the circle with center O then, find the measure of OCP. 
Given that OP = PC.

If AB Is The Tangent To The Circle With center O Then, Find...
  1.    30∘
  2.    45∘
  3.    60∘
  4.    15∘
 Discuss Question
Answer: Option B. -> 45∘
:
B
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
OPC=90
Given,OP = PC.
So,OPCis an isosceles rightangled triangle.PCO=POC
PCO+POC+OPC=180(Angle sum property of a triangle)
PCO+POC+90=180
PCO+POC=90
Hence,POC=OCP=45

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