A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AB= 10 cm, BC = 12 cm and CA = 8 cm, then the lengths of AD, BE and CF respectively will be

Q. In a ∆ABC, perpendicular AD from A and BC meets BC at D. If BD = 8 cm, DC = 2 cm and AD = 4 cm, then

(a) ∆ABC is isosceles
(b) ∆ABC is equilateral
(c) AC = 2AB
(d) ∆ABC is right-angled at A

Join BYJU'S Learning Program

In ΔABC, D is the midpoint of BC and G is the centroid of the triangle. If GD=2 cm, then the length of AD is:

The correct option is A 6 cmCentroid divides the median in the ratio 2:1.AG:GD=2:1So AG=2×GD=2×2=4cmAD=AG+GD=4+2=6cm

In $Δ A B C,$ $D$ is the midpoint of $B C$ and $G$ is the centroid of the triangle. If $G D = 2 c m,$ then the length of $A D$ is:

The correct option is A $6 c m$
Centroid divides the median in the ratio $2 : 1.$
$A G : G D = 2 : 1$
So $A G = 2 \times G D = 2 \times 2 = 4 c m$
$A D = A G + G D = 4 + 2 = 6 c m$