Quantitative Aptitude
MENSURATION MCQs
Regular Polygons, Triangles, Circles
Total Questions : 254
| Page 4 of 26 pages
Answer: Option C. -> OP = 2 AP
:
C
Given that ∠APB=120∘
Also, we know that if two tangents are drawn from an external point to a circle, then the line joining the external point and the centre of the circle bisects the angle between the tangents.
⟹∠APO=∠OPB=60∘
Thus, cos∠OPA=cos60∘=APOP
⟹12=APOP
Thus, OP=2AP
:
C
Given that ∠APB=120∘
Also, we know that if two tangents are drawn from an external point to a circle, then the line joining the external point and the centre of the circle bisects the angle between the tangents.
⟹∠APO=∠OPB=60∘
Thus, cos∠OPA=cos60∘=APOP
⟹12=APOP
Thus, OP=2AP
:
At most one circle can be drawn through a given set of three distinct points. These threepoints will then be referred to as 'concyclic points' (Lying on the same circle). .
Answer: Option D. -> 90∘
:
D
An angle formed by the diameter of a circle at its circumference equals90∘.Hence, the value of x is 90∘.
:
D
An angle formed by the diameter of a circle at its circumference equals90∘.Hence, the value of x is 90∘.
:
The boundary of the circle is called its circumference and the value of circumference is 2πr(where r is the radius of thecircle). If we cut a circle and form a line from it, then the length of the line will be the same as the circumference of the circle.
Answer: Option A. -> 60∘
:
A
Given that ∠BAC=40∘and∠DBC=80∘.
Since the angles formed by the same segment are equal,
∠BDC=∠BAC=40∘.
InΔBDC,
∠BDC+∠DBC+∠BCD=180∘.[Angle sum property]
i.e., 40∘+80∘+∠BCD=180∘
⟹∠BCD=180∘−120∘=60∘
:
A
Given that ∠BAC=40∘and∠DBC=80∘.
Since the angles formed by the same segment are equal,
∠BDC=∠BAC=40∘.
InΔBDC,
∠BDC+∠DBC+∠BCD=180∘.[Angle sum property]
i.e., 40∘+80∘+∠BCD=180∘
⟹∠BCD=180∘−120∘=60∘
Answer: Option D. -> 120∘
:
D
Given thatΔABC is equilateral.
⟹∠BAC=60∘
Since the angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any other point on the remaining part of the circle, we have
∠BOC=2∠BAC=2×60∘=120∘.
:
D
Given thatΔABC is equilateral.
⟹∠BAC=60∘
Since the angle subtended by a chord at the centre of a circle is twice the angle subtended by the same chord at any other point on the remaining part of the circle, we have
∠BOC=2∠BAC=2×60∘=120∘.
Answer: Option C. -> 10 cm
:
C
As the line segment BC passes through the center, it means that it is a diameter of the circle.
Given that radius of the circle = 5 cm
∴ Diameter = 5 + 5 = 10 cm
:
C
As the line segment BC passes through the center, it means that it is a diameter of the circle.
Given that radius of the circle = 5 cm
∴ Diameter = 5 + 5 = 10 cm