Construction of Tangents to a Circle from an External Point

Length of the tangent$=\sqrt{{\left(\mathrm{distance} \mathrm{between} \mathrm{the} \mathrm{external} \mathrm{point} \mathrm{and} \mathrm{the} \mathrm{centre} \mathrm{of} \mathrm{circle}\right)}^2-{\left( \_\_\_\_\_\right)}^2}$ 

If a tangent to a circle of radius $3 \mathrm{cm}$ from a point on the concentric circle of radius $4 \mathrm{cm}$ is $\sqrt{k} \mathrm{cm}$, then find the value of $k$.

If a point lies outside the circle, then two pair tangents will be formed to the circle.

If a point lies inside a circle, there cannot be a tangent to the circle through this point.

A pair of tangents can be constructed from a point $P$ to a circle of radius $4 \mathrm{cm}$ situated at a distance of $4 \mathrm{cm}$ from the centre.

If a tangent to a circle of radius $3 \mathrm{cm}$ from a point on the concentric circle of radius $4 \mathrm{cm}$ is $\sqrt{k} \mathrm{cm}$, then find the value of $k$.

A pair of tangents can be constructed to a circle inclined at an angle of $170°$.

To draw a pair of tangents to a circle which are inclined to each other at an angle of $45°$, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

A pair of tangents can be constructed to a circle inclined at an angle of $190°$.

A tangent to a circle of radius $4 \mathrm{cm}$ from a point on the concentric circle of radius $6 \mathrm{cm}$ is 

To draw two tangents $\mathrm{PA}$ and $\mathrm{PB}$ from an external point $\mathrm{P},$ to a circle of radius $4 \mathrm{cm}$ where angle between $\mathrm{PA}$ and $\mathrm{PB}$ is $65°$, the following steps are given but not in correct order, select the correct order from the options.

Steps of construction:

Step 1 : Draw a circle of radius $4 \mathrm{cm}$ and with centre as $O$.
Step 2  :Draw a perpendicular to $OB$ at point $B$. Let both the perpendiculars intersect at point $P$. $PA$ and $PB$ are the required tangents at an angle of $65°$.
Step 3 : Draw a radius $OB$, making an angle of $115°=(180°-65°)$ with $OA$.
Step 4 : Take a point $A$ on the circumference of the circle and join $OA$. Draw a perpendicular to $OA$ at point $A$.

The construction steps to draw a pair of tangents to the circle of radius $6 \mathrm{cm}$ from a point $10 \mathrm{cm}$ away from its centre, are given below but not in correct order, select the correct order from the options below.

A pair of tangents to the given circle can be constructed as follows.

Step 1: Taking M as centre and MO as radius, draw a circle.
Step 2: Let this circle intersect the previous circle at point Q and R.
Step 3: Taking any point O of the given plane as centre, draw a circle of $6 \mathrm{cm}$ radius. Locate a point P, $10 \mathrm{cm}$ away from O. Join OP.
Step 4: Bisect OP. Let M be the mid-point of PO.
Step 5: Join PQ and PR. PQ and PR are the required tangents.

Draw a circle of radius $3 \mathrm{cm}$. Construct a pair of tangents from an exterior point $5 \mathrm{cm}$ away from its centre.

Draw a chord of length $2.3 \mathrm{cm}$ in a circle of radius $13.1 \mathrm{cm}$ and draw the tangent to its both ends. 

A pair of tangents can be constructed from a point $P$ to a circle of radius $3.5 \mathrm{cm}$ situated at a distance of $3 \mathrm{cm}$ from the centre.

A pair of tangents can be constructed to a circle inclined at an angle of $170°$.

Draw a circle of radius $6 \mathrm{cm}$. From a point $8 \mathrm{cm}$ away from its centre, construct the pair of tangents to the circle. Below given are the steps for construction. Arrange them in order 

A. Taking $\mathrm{M}$ as centre and $\mathrm{MO}$ as radius draw a circle 

B. Join $\mathrm{PQ}$ and $\mathrm{PR}.$

C. Taking any point $\mathrm{O}$ as centre draw a  circle of $6 \mathrm{cm}$ radius-locate a point P, $8 \mathrm{cm}$ away from $\mathrm{O}.$

D. Bisect $\mathrm{PO},$ and let $\mathrm{M}$ be the midpoint of $\mathrm{PO}.$

E. The circle interests the previous circle at points $\mathrm{Q}$ and $\mathrm{R}.$