Tag: maths

Questions Related to maths

$\triangle ABC$ is inscribed in a circle. Point $P$ lies between $A$ and $C$, whereas point $Q$ lies between $B$ and $C$. If $m(\text{arc}\, APC) = 60^\circ$ and $\angle BAC = 80^\circ$, find $m(\text{arc}\, BQC)$.
maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $180^\circ$

  2. $90^\circ$

  3. $160^\circ$

  4. $120^\circ$

Show answer
Correct Option: C
Explanation:

By inscribed angle theorem, 

$ \cfrac 12 m\angle BAC = m(arc BQC)$
$m(arc BQC) = 2 \times \angle BAC$
$\therefore m(arc BQC) = 2 \times 80^o = 160^o$

Which of the following is not a sector of a circle?

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. Pizza slice

  2. Cathedral window

  3. Birthday cap

  4. Apple pie

Show answer
Correct Option: C
Explanation:

Pizza slice, Cathedral window and apple pie are sector of a circle 

whereas Birthday cap is of conical shape which is not a sector of circle.
Hence option 'C' is correct choice 

Circular dome is a 3D example of which kind of sector of the circle?

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. Quadrant

  2. Semicircle

  3. Octant

  4. Sextant

Show answer
Correct Option: B
Explanation:

A circular dome is a 3 dimension structure of a semicircle.

What is the largest number of non-overlapping sectors that can be created when a circle is crossed by three straight lines?

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. 3

  2. 4

  3. 6

  4. 7

Show answer
Correct Option: D

Points $A,B,C $ are on a circle, such that $m(arc AB)=m(arc BC)=^o$. No point, except point $B$, is common to the arcs.which is the type of $\triangle ABC$?

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. Equilateral triangle

  2. Scalene triangle

  3. Right angled triangle

  4. Isosceles triangle

Show answer
Correct Option: A

Find the area of a sector of a circle with radius $6$cm if angle of the sector is $60^o$.

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $6\pi$

  2. $7\pi$

  3. $3\pi$

  4. $5\pi$

Show answer
Correct Option: A
Explanation:
Area of sector of circle $=\dfrac{\theta}{360}\times \pi r^2$
$=\dfrac{60}{360}\times \pi\times (6)^2$
$=\dfrac{1}{6}\times \pi\times (36)$
$=6\pi$.

Consider a circle with unit radius. There are seven adjacent sectors, $S _1, S _2, S _3, ............ S _7$, in the circle such that their total area is $\dfrac {1}{8}$ of the area of the circle. Further, the area of the $j^{th}$ sector is twice that of the $(j-1)^{th}$ sector, for $j$ $=$ $2, ........... 7$. What is the area of sector $S _1?$

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $\displaystyle \frac{\pi }{508}$

  2. $\displaystyle \frac{\pi }{2040}$

  3. $\displaystyle \frac{\pi }{1016}$

  4. $\displaystyle \frac{\pi }{1524}$

Show answer
Correct Option: C
Explanation:

Let the area of thesector S$ _1$ be x units. Then, the area of the corresponding sectors shall be 2x, 4x, 8x, 16x, 32x and 64x. The total area then shall be 127x units. This is $\displaystyle \frac{1}{8}$ of the total area of the circle. 

Hence, the total area of the circle will be $127x \times 8 = 1,016 x\ units.$
$\Rightarrow 1016 x = \pi (1)^2 \Rightarrow x = \pi/1016$
Hence area of sector $S _1 $ is $\pi / 1016$

The angle subtended by the chord AB in the minor arc of S is - 

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $\dfrac{3 \pi}{4}$

  2. $\dfrac{5 \pi}{6}$

  3. $\dfrac{2 \pi}{3}$

  4. $\dfrac{ \pi}{4}$

Show answer
Correct Option: A

The length of minor arc $\overset{\frown}{AB}$ of a circle is $\dfrac{1}{4}$ of its circumference, then the measure of the angle subtended by the minor arc $\overset{\frown}{AB}$ will be ....

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. 30

  2. 45

  3. 90

  4. 60

Show answer
Correct Option: A

Let a semicircle with centre O and diameter AB. Let P and Q be points on the semicircle and R be a point on AB extended such that OA =QR < PR. If $\widehat{POA} = 102^0$ then $\widehat{PRA} $ is 

maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

  1. $51^0$

  2. $34^0$

  3. $25.5^0$

  4. not possible to be determined

Show answer
Correct Option: D
Explanation:


Since R can be any point between A & R' & hence its corresponding point Q will lie on the arc AQ'. Hence, $\angle$ PRA can not be uniquely determined.