In triangle ABC, point L and M divides the side AB and BC in the ratio 2:3 respectively AM - Maths -

Question

In triangle ABC, point L and M divides the side AB and BC in the
ratio 2:3 respectively
AM and LC intersect at point P From point P a line parallel to BA
is drawn intersectingAC at D Find the ratio AD: DC Please explain
with diagram

Gursheen kaur. · Accepted Answer

$Δ A L P \sim Δ P Q M (b y A A s i m i l a r i t y) \frac{P L}{P Q} = \frac{L A}{Q M} = \frac{2 x}{Q M} ......... (i) Δ C Q M \sim Δ C L B (b y A A s i m i l a r i t y) \frac{Q M}{L B} = \frac{M C}{B C} \frac{Q M}{3 x} = \frac{3 y}{5 y} Q M = \frac{9 x}{5} ........... (i i) p u t (i i) i n (i), w e g e t, \frac{P L}{P Q} = \frac{2 x}{9 x / 5} \frac{P L}{P Q} = \frac{10}{9} ........... (i i i) n o w, i n Δ C L B, a s Q M i s t h e m i d s e g m e n t, t h e r e f o r e, b y u \sin g m i d p o int t h e o r e m, L Q = 2 z, Q C = 3 z \Rightarrow P L + P Q = L Q = 2 z f r o m e q u a t i o n (i i i), w e h a v e, P L = \frac{10}{19} 2 z ............. (i v) P Q = \frac{9}{10} 2 z \Rightarrow P C = P Q + Q C = \frac{9}{10} 2 z + 3 z = \frac{75 z}{19} .... (v) f r o m (i v) & (v), w e g e t, P L : P C = 4 : 15 s i m i l a r l y, b y u \sin g m i d p o int t h e o r e m, i n t r . C A L, w e h a v e, A D : D C = 4 : 15$

In triangle ABC, point L and M divides the side AB and BC in the ratio 2:3 respectively.AM and LC intersect at point P. From point P a line parallel to BA is drawn intersectingAC at D. Find the ratio AD: DC. Please explain with diagram.

In triangle ABC, point L and M divides the side AB and BC in the ratio 2:3 respectively.
AM and LC intersect at point P. From point P a line parallel to BA is drawn intersectingAC at D. Find the ratio AD: DC. Please explain with diagram.