Quantitative Aptitude
MENSURATION MCQs
Regular Polygons, Triangles, Circles
Total Questions : 254
| Page 9 of 26 pages
Answer: Option A. -> Diameter
:
A
A chord is a line which touches the circle at two distinctpoints on its circumference.
A segment is an area cut by a chord in a circle and hence cannot be a chord.
An arc is a part of the circumference and hence cannot be a chord.
The radius is not a chord asit does not touch the circle at two points on its circumference.
The diameter isa chord since it touches the circle at two points on its circumference.
:
A
A chord is a line which touches the circle at two distinctpoints on its circumference.
A segment is an area cut by a chord in a circle and hence cannot be a chord.
An arc is a part of the circumference and hence cannot be a chord.
The radius is not a chord asit does not touch the circle at two points on its circumference.
The diameter isa chord since it touches the circle at two points on its circumference.
Answer: Option B. -> 180∘
:
B
The opposite angles of a cyclic quadrilateral are supplementary to each other. Hence, the sum of opposite angles in a cyclic quadrilateral is 180∘.
:
B
The opposite angles of a cyclic quadrilateral are supplementary to each other. Hence, the sum of opposite angles in a cyclic quadrilateral is 180∘.
Answer: Option B. -> cyclic quadrilateral
:
B
A quadrilateral is called cyclic if all the four vertices of it lie on a circle and the sum of its opposite anglesis 180∘.
:
B
A quadrilateral is called cyclic if all the four vertices of it lie on a circle and the sum of its opposite anglesis 180∘.
Answer: Option C. -> 50∘
:
C
In the figure, ∠ABD=50∘
Since the angles subtended by an arc in the same segment are equal, we have ∠ABD=∠ACD.
⇒X=∠ACD=50∘
:
C
In the figure, ∠ABD=50∘
Since the angles subtended by an arc in the same segment are equal, we have ∠ABD=∠ACD.
⇒X=∠ACD=50∘
Answer: Option A. -> True
:
A
The linedrawn through the centre of a circleperpendicularlybisects a chord.
Hence, ∠x=90∘.
:
A
The linedrawn through the centre of a circleperpendicularlybisects a chord.
Hence, ∠x=90∘.
Answer: Option C. -> Parallelogram
:
C
A quadrilateral is cyclic ifits opposite angles are supplementary.
In square, rectangle and isosceles trapezium, the opposite angles are supplementary, that is, the sum of the opposite angles is180∘.
In a parallelogram, the opposite angles are equal and may not add to180∘. Hence, a parallelogram cannot be a cyclic quadrilateral.
:
C
A quadrilateral is cyclic ifits opposite angles are supplementary.
In square, rectangle and isosceles trapezium, the opposite angles are supplementary, that is, the sum of the opposite angles is180∘.
In a parallelogram, the opposite angles are equal and may not add to180∘. Hence, a parallelogram cannot be a cyclic quadrilateral.
Answer: Option D. -> circle
:
D
Circle is the set of all the points in a plane which are at a given distance from a fixed point in the plane. That fixed point is known as thecentre of thecircle.
:
D
Circle is the set of all the points in a plane which are at a given distance from a fixed point in the plane. That fixed point is known as thecentre of thecircle.
Answer: Option B. -> 40∘
:
B
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Given∠ABC=50∘,
∴∠AOC=2∠ABC=2×50∘=100∘
Also, since OA and OC are radii of the circle, OA=OC.
⟹∠OAC=∠OCA
In△AOC,
x+x+∠AOC=180∘.
⟹2x=180∘−∠AOC=180∘−100∘=80∘
⟹x=40∘
:
B
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Given∠ABC=50∘,
∴∠AOC=2∠ABC=2×50∘=100∘
Also, since OA and OC are radii of the circle, OA=OC.
⟹∠OAC=∠OCA
In△AOC,
x+x+∠AOC=180∘.
⟹2x=180∘−∠AOC=180∘−100∘=80∘
⟹x=40∘
:
Chord is a line segment that joins two points on the circumference of a circle.Diameter is the longest chord of a circle which passes through centre joining the two points on the circumferenceof a circle.
Answer: Option C. -> 30∘,150∘
:
C
In ΔOAB,
AB = OA = OB = radius of the circle.
∴ΔOAB is an equilateral triangle.
Therefore, each interior angle of this triangle will be equal to 60∘.
∴∠AOB=60∘.
Since the angle subtended by an arc of the circle at its centre is double the angle subtended by it at any point on the remaining part of the circle, we have
∠ACB=12∠AOB=12×60∘=30∘.
Now in the cyclic quadrilateral ACBD,
∠ACB+∠ADB=180∘. [Opposite angles in a cyclic quadrilateral are supplementary]
∴∠ADB=180∘−∠ACB=180∘−30∘=150∘
Therefore, the angles subtended by thechord AB at a point on the major arc and the minor arc are 30∘ and 150∘ respectively.
:
C
In ΔOAB,
AB = OA = OB = radius of the circle.
∴ΔOAB is an equilateral triangle.
Therefore, each interior angle of this triangle will be equal to 60∘.
∴∠AOB=60∘.
Since the angle subtended by an arc of the circle at its centre is double the angle subtended by it at any point on the remaining part of the circle, we have
∠ACB=12∠AOB=12×60∘=30∘.
Now in the cyclic quadrilateral ACBD,
∠ACB+∠ADB=180∘. [Opposite angles in a cyclic quadrilateral are supplementary]
∴∠ADB=180∘−∠ACB=180∘−30∘=150∘
Therefore, the angles subtended by thechord AB at a point on the major arc and the minor arc are 30∘ and 150∘ respectively.
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