Important Terms Related to a Circle

A chord $AB$ of a circle of radius $10 \mathrm{cm}$ makes a right angle at the centre of the circle. Find the difference between the areas of the major and minor segments of the circle. (use $\mathrm{\pi } = 3.14$)

AB is a chord to a circle and PAT is the tangent to the circle at A. If $\angle BAT=75°$ and $\angle BAC=45°$, C being a point on the circle then, $\angle ABC$ is equal to-

What is the length of the radius of the circumcircle of the equilateral triangle, the length of whose side is $6\sqrt{3} \mathrm{cm}$?

In a quadrilateral $\mathrm{ABCD}$, the bisectors of $\angle A$ and $\angle B$ meet at $O$. If $\angle C=70°$ and $\angle D=130°$, then find the measure of $\angle AOB$.

The diagonals $AC$ and $BD$ of cyclic quadrilateral $ABCD$ intersect each other at point $P$ then which expression follow?

Find the length of the chord $AC$ where $AB$ and $CD$ are the two diameters perpendicular to each other of a circle with radius $4\sqrt{2} \mathrm{cm}$ and also find $\angle OAC$ and $\angle OCA$.

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 figure, $ABCD$ is a unit square. A circle is drawn with centre $O$ on the extended line $CD$ and passing through $A.$ If the diagonal $AC$ is tangent to the circle, then the area of the shaded region is

Let $AB$ be a line segment of length $2.$ Construct a semicircle $S$ with $AB$ as diameter. Let $C$ be the midpoint of the arc $AB\mathit{.}$ Construct another semicircle $T$ external to the triangle $ABC$ with chord $AC$ as diameter. The area of the region inside the semicircle $T$ but outside $S$ is

Seven cookies of radius $1$ inch are cut from a circle of cookie dough, as shown. Neighboring cookies are tangent, and all except the center cookie are tangent to the edge of the dough. The leftover scrap is reshaped to form another cookie of the same thickness. The radius in inches of the scrap cookie is

In the figure below, $n$ congruent semicircles are drawn along a diameter of a large semicircle, with their diameters covering the diameter of the large semicircle with no overlap. Let $A$ be the combined area of the small semicircles and $B$ be the area of the region inside the large semicircle but outside the small semicircles. The ratio $A:B$ is $1:18$. What is $n$?

The area of the minor segment of a circle is $41$ square units and the area of major segment of a circle is $57$ square units. Find the area of the circle

The area of the minor segment of a circle is $30$ square units and the area of major segment of a circle is $57$ square units. Find the area of the circle

The area of the minor segment of a circle is $25$ square units and the area of major segment of a circle is $27$ square units. Find the area of the circle

The area of the minor segment of a circle is $50$ square units and the area of major segment of a circle is $100$ square units. Find the area of the circle

Write the exterior points of the following circle

Write the exterior points of the following circle

A chord of a circle of radius $10 \mathrm{cm}$ subtends a right angle at the centre. Find the area of the major sector.

Find the area of the sector of a circle with radius $2 \mathrm{cm}$ and an angle of $20°$. Also, find the area of the corresponding major sector. (Use $\mathrm{\pi }=3.14$)