Concurrent Lines and Related Theorems

For a right-angled triangle, $O$ is the circumcentre of the triangle $∆ABC$. Now, $BO=8.5 \mathrm{cm}$, find the length of $BC$(in $\mathrm{cm}$)?

In the figure, $XY$ is the bisector of $\angle ZXW$. $\angle ZXY=75°$, $\angle PXW$ is _____$°$

In the figure, $OB$ is the bisector of $\angle AOC$. Find $\angle AOB$(in degrees)

The sides of a triangle is $27 \mathrm{cm}, 36 \mathrm{cm}$ and $45 \mathrm{cm}$. The inradius of the triangle is 

The sides of the triangle are $9 \mathrm{cm},15 \mathrm{cm}$ and $18 \mathrm{cm}$. Its area is $67.35 \mathrm{sq}.\mathrm{cm}.$The inradius (up to $2$ decimal places) of the triangle is _____$\mathrm{cm}$

The inradius of the triangle whose sides are $13 \mathrm{cm},14 \mathrm{cm}$ and $15 \mathrm{cm}$ is _____

Find inradius (in $\mathrm{cm}$) of a triangle whose sides are $32 \mathrm{cm},24 \mathrm{cm}$ and $40 \mathrm{cm}$.

Find inradius(in $\mathrm{cm}$) of an equilateral triangle whose side is $7 \mathrm{cm}$?

The non-concurrent lines $EF,GH$ and $KL$ intersect at _____.

The lines $XY$ and $PQ$ are _____lines.

Define non concurent lines with example

For the equilateral triangle, find the position of the incentre.

For the equilateral triangle, find the position of the circumcentre.

In an equilateral triangle $∆XYZ$, the circumcentre, orthocentre and incentre are ______

The radius of a circle is $16 \mathrm{cm}$. Find the radius of the pedal triangle.

What is pedal triangle?

State converse of Ceva's thorem

If $D,E$and $F$ are three points on the sides of the triangle and$\frac{BE}{EC}\times \frac{CF}{AF}\times \frac{AD}{DB}=1$. Then, the points $D,E$ and $F$ are _____

In the triangle $∆ABC$, $AP,BQ$ and $CR$ are concurrent at $O$. Then, $\frac{BP}{PC}\times \frac{QC}{QA}\times \frac{AR}{RB}=$_____

Prove Ceva's theorem.