Construction using given Information

Find the length of mean proportion of the line segments of length $4 \mathrm{cm}$ and $3 \mathrm{cm}$.

Find the length of the mean proportion of $10 \mathrm{cm}$ and $4 \mathrm{cm}$ by geometric method.

Find the value of $\sqrt{35}$ by geometric method. (Correct up to one decimal place)

The construction of incircle is being done by obtaining the point of intersection of two perpendicular of sides and bisector of two angles. 

The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches the three _____. (angles/sides)

The circumscribed circle or circumcircle of a polygon is a circle that passes through all the _____ of the polygon. (sides/vertices)

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 $k$.

The bisectors of angles $\mathrm{A}$ and $\mathrm{B}$ of a scalene triangle $\mathrm{ABC}$ meet at $\mathrm{O}.$ What is the point $\mathrm{O}$ called?

Perpendicular bisectors of the sides $\mathrm{AB}$ and $\mathrm{AC}$ of a triangle $\mathrm{ABC}$ meet at $\mathrm{O}$. What do you call the point $\mathrm{O}$?

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 $k$.

The bisectors of angles $\mathrm{A}$ and $\mathrm{B}$ of a scalene triangle $\mathrm{ABC}$ meet at $\mathrm{O}.$

$\mathrm{OR}$ and $\mathrm{OQ}$ are drawn perpendiculars to $\mathrm{AB}$ and $\mathrm{CA}$ respectively. What is the relation between $\mathrm{OR}$ and $\mathrm{OQ} ?$

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 

Construct a triangle $ABC$ with $AB=5 \mathrm{cm}$, $\angle B=60°$ and $BC=6.4 \mathrm{cm}$. Draw the incircle of the triangle $ABC$.