Construction of Circumcircle and Incircle

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 the radius of the incircle of a right triangle having perpendicular sides of length $5$ centimetres and $12$ centimetres is $k$ cm, then find the value of $k$.

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

Construct an incircle of an equilateral triangle with side $4.6 \mathrm{cm}$.

Construct an incircle of a right angle $△ABC$ with sides $8 \mathrm{cm},6 \mathrm{cm}$ and $10 \mathrm{cm}$.

The point equidistant from the vertices of triangle is called

Construct a $△ABC$ in which $AB=6 \mathrm{cm}, BC=4 \mathrm{cm}$ and $\angle B=120°$. Also construct the incircle of the triangle. 

Draw a circumcircle of a triangle whose sides are $5 \mathrm{cm}, 4.5 \mathrm{cm}$ and $7 \mathrm{cm}$. Where and why does its circumcentre lie?

Draw a circumcircle of a triangle with sides respectively $5 \mathrm{cm}, 12 \mathrm{cm}$ and $13 \mathrm{cm}$. Why does its circumcentre fall at the side of length $13 \mathrm{cm}$?

Construct an incircle of a triangle with $AB=4.6 \mathrm{cm}, AC=4.2 \mathrm{cm}$ and $\angle A = 90°$.

Construct an incircle of an equilateral triangle with side $4.6 \mathrm{cm},$ Is its incentre and circumcentre are coincidence? Justify your answer.

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

The circumcentre of the triangle lies inside, if the triangle is an acute triangle. 

If the triangle is obtuse angled, its circumcentre will fall at one of its sides.

All three sides of a triangle touch its incircle. 

Circumcircle and incircle of an equilateral triangle can be drawn from the same centre. 

Prove that bisector of any angle of triangle and perpendicular bisector of its opposite side if intersect each other then it intersect on circumcircle.