Exercise

Two concentric circles of radii $5 \mathrm{cm}$ and $3 \mathrm{cm}$ are drawn. Find the length of the chord of the larger circle which touches the smaller circle.

Express your answer in centimetres(cm).

Prove that the parallelogram circumscribing a circle is a rhombus.

A triangle $\mathrm{ABC}$ is drawn to circumscribe a circle of radius $3 \mathrm{cm}$ such that the segments $\mathrm{BD}$ and $\mathrm{DC}$ into which $\mathrm{BC}$ is divided by the point of contact $\mathrm{D}$ are of length $9 \mathrm{cm}$ and $3 \mathrm{cm}$ respectively (See adjacent figure). Find the sides $\mathrm{AB}$ and $\mathrm{AC}$.

Draw a circle of radius $6 \mathrm{cm}.$From a point $10 \mathrm{cm}$ away from its centre, construct the pair of tangents to the circle and measure their lengths. Verify by using Pythagoras Theorem.

Construct a tangent to a circle of radius $4 \mathrm{cm}$ from a point on the concentric circle of radius $6 \mathrm{cm}$ and measure its length. Also verify the measurement by actual calculation.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle and measure them. Write your conclusion.

In a right triangle $ABC$, a circle with a side $AB$ as diameter is drawn to intersect the hypotenuse $AC$ in $P$. Prove that the tangent to the circle at $P$ bisects the side $BC$.

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Draw a tangent to a given circle with centre $\mathrm{O}$ from a point $\text{'}\mathrm{R}\text{'}$ outside the circle. How many tangents can be drawn to the circle from that point?

[Hint: The distance of two points to the point of contact is the same.]