Angle Made by a Segment of a Circle

If an angle formed by an arc at the centre of a circle is $100°$, then find the angle formed by the same arc at any point on the remaining part of the circle.

A canal is surrounding a circular city of diameter $4$ kilometres. Four lampposts are located on the border of the city close to the canal at locations $A, B, C$ and $D$, such that a direct path from $A$ to $C$ cuts another direct path from $B$ to $D$ perpendicularly at a junction $E$. The value$E{A}^2+E{B}^2+E{C}^2+E{D}^2$ is

What is the difference between radius of curvature and radius?

A circle is divided into $5$ sectors with area equal to $1:2:3:4:5$. Find the angle subtended at the center of the circle by the largest sector.

The triangle $ABC$ is inscribed in a circle. The bisectors of the angles $\angle BAC, \angle ABC \text{and} \angle ACB$ intersect at the points $X,Y \text{and} Z$ on the circle respectively. Prove that in $∆XYZ$, $\angle YXZ=90°-\frac{1}{2}\angle BAC$

In the given figure, $\mathrm{O}$ is the centre of the circle. If $\angle ADC=118°$, then the value of $x$ is :

In figure, $\mathrm{PQ}$ is the diameter of the circle with centre $\mathrm{O}$. If $\angle \mathrm{PQR}=65°, \angle \mathrm{RPS}=40°$ & $\angle \mathrm{PQM}=50°$, find $\angle \mathrm{QPR}, \angle \mathrm{PRS} \& \angle \mathrm{QPM}$.

Jaspreet draws $5$ circles as shown in the figure below.

Jaspreet claims, “These five circles are concentric as they have a common point.”

Do you agree? Give a reason to justify your answer.

Two circles $C1$ and $C2$ are drawn from the same centre. The diameter of $C1$ is $6 cm$, which is one-third of the diameter of$C2$ . What is the length of the radius of $C2$?

Jasleen adds a line segment $RQ$ to the circle.

The length of $RQ$ is equal to the length of $AB$.

Is $RQ$ a chord of the circle? Give a reason to justify your answer.

Jasleen draws a circle of radius $3.8 cm$ with centre $C$

She wants to draw a perpendicular bisector to the chord $AB.$

Which of the following cannot be true for the perpendicular bisector of the chord?

In the given figure, O is the centre of the circle, find the value of x

In the given figure $O$ is the centre of the circle. Prove that $\angle x+\angle y=\angle z$

In the circle, seg $AB$ is a diameter. Point $C$ is in the interior of the circle. Prove that $\angle ACB$ is an obtuse angle.

In the figure, if $\angle ABC=50°$ and $\angle BDC=40°$, calculate $\angle BCA$.

In the figure, if $\angle ABC=50°$ and $\angle BDC=40°$, calculate $\angle BAC$.

In the figure, if $\angle ABC=50°$ and $\angle BDC=40°$, calculate $\angle CDA$.

In the given figure, $O$ is centre and $\angle ABO=30°$, then $\angle ACB$ is

Find the angle $y$ from the diagram.

$A, B$and $C$ are three points on the circle with centre $O$ such that $\angle AOB=90°$ and $\angle AOC=110°$. Find $\angle BAC$.