Introduction to Circles

Round Objects around us are

Write the round objects around our surroundings.

In the adjoining figure, $C$ is the centre of the circle. The tangent to the circle of radius $6 \mathrm{cm}$ from a point $P$ outside the circle is of length $8 \mathrm{cm}$. If the distance of the point $P$ from the farthest point of the circumference is $k \mathrm{cm}$, then find the value of $k$.

In the picture below, a square is drawn with its vertices on a circle. If the perimeter of the circle is $2\mathrm{\pi }\sqrt{\mathrm{k}} \mathrm{cm}$ then find $k$.

A copper when bent in the form of a square encloses an area of $121 {\mathrm{cm}}^2$. If the same wire is bent into the form of a circle, find the area of the circle in ${\mathrm{cm}}^2$.

If the circumference of a circle which has an area of $144\mathrm{\pi } {\mathrm{cm}}^2$ is $k\mathrm{\pi }$, then find the value of $k$.

Trace a circle with the help of some other things other than the bangle in your notebook or the ground. Which thing makes the smallest circle? Which thing makes the biggest circle?

A bangle can be used to trace a circle. What are the other things around you that you can use to trace a circle?

In the following figure, a circle is inscribed in the quadrilateral $\mathrm{ABCD}.$

If $\mathrm{BC}=38\mathrm{cm},$ $\mathrm{QB}=27\mathrm{cm},$ $\mathrm{DC}=25\mathrm{cm}$ and that $\mathrm{AD}$ is perpendicular to $\mathrm{DC},$ find the radius of the circle.

In the figure below ‘r’ is the radii and ‘O’ is centre of the circles. Points, A, B, P, Q, X and Y lie on the respective circles.

PQ = 5 cm, m∠AOB = m∠XOY = 60$ °$.

Which of the following arcs are congruent to each other?

In the figure below, points A, C, D and E lie on the circle.

Of all line segments shown in the figure above, _____ is the chord of the circle.

In the given figure, O is the centre of the circle and points P, Q and R are points on the circumference.

The value of x is _____ degrees.

Is the given shape a circle?

By definition, radius is the straight line passing through the center of a circle connecting two points on the boundary of the circle. Is this statement true or false?

Identify the radius of the given circle.

Which of the points do you think is not true with radius of a circle?

1. Radius of a circle is the line segment joining the center of the circle and any point on the boundary of a circle

2. For a given circle we can have one and only one radius.

3. Radius of a circle is the line segment joining any two points on the boundary of the circle

4. Radius of a circle measures half the diameter.