Measurements in Circle

Area of major sector is smaller than that of a semicircle.

Define central angle of a circle?

If the length of minor arc is $20 \mathrm{cm}$ and length of major arc is $60 \mathrm{cm}$.Then, find the circumference of the circle.

Area of minor sector is less than that of a semicircle.

 Find the area of the major segment of a circle if the area of the corresponding minor segment is $62 \mathrm{sq}. \mathrm{units}$ and the radius is $14$units. Use $\mathrm{\pi }=\frac{22}{7}$ and write the answer in $\mathrm{sq}. \mathrm{units}$.

Calculate the area of the minor sector of a circle if the area of its major sector is $44 \mathrm{sq}.\mathrm{units}$ and the radius is $5 \mathrm{units}$. Use $\mathrm{\pi }=\frac{22}{7}$.

Calculate the area of the major sector of a circle if the area of its minor sector is $54 \mathrm{sq}.\mathrm{units}$ and the radius is $7 \mathrm{units}$. Use $\mathrm{\pi }=\frac{22}{7}$.

The arc of a circle is a line segment.

The area of a circle is $220 {\mathrm{cm}}^2$. If area of the square inscribed in it is $k {\mathrm{cm}}^2$, then find the value of $k$. Use $\left(\mathrm{\pi }=\frac{22}{7}\right)$

If the diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24 \mathrm{cm}$ and $7 \mathrm{cm}$ is $k \mathrm{cm}$, then find the value of $k$

In the following diagram, the plane figure $ABCD$ is part of a sector of a circle.

$OA=AB=8 \mathrm{cm}$ and $A\hat{O}D=\theta °$

Given that the area of $ABCD$ is $200{ \mathrm{cm}}^2$. Determine the value of $\theta$. Give your answer correct to the nearest degree. [Enter the value excluding units]

The diagram shows a triangular field $ABC$. A farmer tethers his horse at point $A$ with a rope of length $85 \mathrm{m}$.

Find, correct to $3$ significant figures., the area of the field that the horse cannot reach.

A circular sector has radius $4 \mathrm{cm}$ and a corresponding arc length of $1.396 \mathrm{cm}$ rounded to the nearest thousandth of a centimetre. Find the area of the sector. [Enter the value correct up to three significant figures excluding units]

A sector of a circle has a radius of $5 \mathrm{cm}$ and central angle measuring $45°$. Find the area of the sector and the length of the arc.

A landscaper builds a regular hexagonal patio in a circular garden. The area not covered by the patio will be covered in grass. The radius of the garden is $1.5 \mathrm{m}$. Find the area covered by grass in the garden. Find the area covered by the grass in the garden up to three significant figures.      [Enter the value excluding units correct up to three significant figures]

A racetrack is in the form of a ring whose inner circumference is $352 \mathrm{m}$ and outer circumference is $396 \mathrm{m}$. If the width of the track is $A \mathrm{m}$ and the area of the track is $B {\mathrm{m}}^2$, then find the value of $A+B$ considering $\mathrm{\pi }=\frac{22}{7}$.

The length of the common chord of two intersecting circles is $30 \mathrm{cm}.$ If the radii of the two circles are $25 \mathrm{cm} \mathrm{and} 17 \mathrm{cm},$ find the distance between their centres.

The radii of two concentric circles are $17 \mathrm{cm} \mathrm{and} 10 \mathrm{cm},$ a line PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If $QR=12 \mathrm{cm},$ calculate PQ.

In given figure, CD is a diameter which meets the chord AB at E such that $AE=BE=4 \mathrm{cm}. \mathrm{If} CE=3 \mathrm{cm},$ find the radius of the circle.

An isosceles triangle $ABC$ with $AB=AC=25 \mathrm{cm} \mathrm{and} BC=14 \mathrm{cm}$ is inscribed in a circle. Calculate the radius of the circle. (Answer up to two places of decimal)