Circle through Three Points

Two number of circles can be passing through three different non-collinear points.

Draw a pair of circles having two common points.

Maximum number of common points when two circles joined is 

How many number of circles can be passing through three different non-collinear points.

Draw a pair of circles having one common point.

If the length of circum radius of a right angle triangle is $10 \mathrm{cm}$ then the length of hypotenuse is $25 \mathrm{cm}$.

The centre of a system of concentric circle is same.

Perpendicular bisectors of the sides $\mathrm{AB}$ and $\mathrm{AC}$ of a triangle $\mathrm{ABC}$ meet at $\mathrm{O}$. What is the relation between the distances $\mathrm{OA},\mathrm{OB}$ and $\mathrm{OC}$?

Circles concentric to each other have different centres.

Draw two concentric circles of radius $3 \mathrm{cm}$ and $5 \mathrm{cm}$. Construct a tangent to smaller circle from a point on the larger circle.

Two circles or more circles are called _____ circles if and only if they have same centre and different radii.

$C$ is the centre of a circle of radius $10 \mathrm{cm}$. $A$ is any point in the circle such that $AP=6 \mathrm{cm}.$ $P$ is a point moving along the circumference such that $PA=x$, then what are the positions of the points $C, A$ and $P$ at these values?

$C$ is the centre of a circle of radius $10 \mathrm{cm}$. $A$ is any point in the circle such that $AP=6 \mathrm{cm}.$ $P$ is a point moving along the circumference such that $PA=x$, then what are the minimum and maximum values of $x$ in cm ?

In the figure below, $AD=AB, CD=BC$.

Which of these statements is true about quadrilateral $ABCD$?

In the figure below, points $A, B, C$and $D$ lie on the circle. $BE$ and $DE$ are bisectors of $\angle ABC$ and $\angle ADC$ respectively.

What is the sum of the measures of $\angle BAD$ and $\angle BCD$?

In the figure below, points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ lie on the circle. $\mathrm{BE}$and $\mathrm{DE}$ are bisectors of $\angle \mathrm{ABC}$ and $\angle \mathrm{ADC}$ respectively.

What is the sum of the measures of $\angle \mathrm{CDE}$ and $\angle \mathrm{CBE}$?

In the quadrilateral

$ABCD$ below,$m\angle ADC :m\angle BAD=3:4$.

The measure of $\angle ADC = {90}^{°}$. What is the measure of $\angle BAD$?

In the figure below, $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are points on the circle.

Which of these statements is true about quadrilateral $\mathrm{ABCD}$?

In the figure below, $A, B, C$ and $D$ are points on the circle.

$AD=AB, CD=BC$.

What is the measure of $\angle ADC$?

In the figure below, $\mathrm{AE}$ is the diameter of the circle. $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are points on the circle. The measure of $\angle \mathrm{ABC} = {140}^{°}.$

What is the measure of $\angle \mathrm{CAE}$?