A $20$-feet ladder leans against a wall at height of $16$ feet from the ground. How far is the base of the ladder from the wall?

Find $LM, MN, LN$ and also the area of $∆LON$.

$∆ABC$ is equilateral and $CD$ of the right triangle $BCD$ is $8 \mathrm{cm}$. Find the side of the equilateral $∆ABC$ and also $BD$.

In the figure, $ABC$ is a triangle and $AM$ is one of its medians. If $BM = 3.5 \mathrm{cm}$, find the length of the side $BC$.

In the figure $G$ is the centroid of the triangle $XYZ$.

If $GL=2.5 \mathrm{cm}$, find the length $XL$.

In the figure $G$ is the centroid of the triangle $XYZ$.

If $YM=9.3 \mathrm{cm}$, find the length $GM$.

$ABC$ is a triangle and $G$ is its centroid. If $AD=12 \mathrm{cm}, BC=8 \mathrm{cm}$ and $BE=9 \mathrm{cm}$, find the perimeter of $∆BDG$.

In $∆ABC,S$ is the circumcentre, $BC=72 \mathrm{cm}$ and $DS=15 \mathrm{cm}$. Find the radius of its circumcircle.

Identify the incentre of the triangle $PQR$.