In a ΔABC, points D and E are lying on AB and AC, respectively. DE is also parallel to the base BC. O is the intersection of BE and CD. If AD : DB = 4 : 3 find the ratio of DO to DC.

Question

Question

This question was previously asked in

RRC Group D Previous Paper 4 (Held On: 22 Sep 2018 Shift 1)

Answer 1

Concept:

Similar triangles:

Similar triangle are triangles that have the same shape, but their sizes may vary.

Properties:

Calculation:

F1 S.G M.P 19 July 2019 D 1

In ΔADE and ΔABC

∠A is common

∠D = ∠B and ∠E = ∠C

∴ ΔADE ∼ ΔABC

According to similar triangle property

\(\frac{{AD}}{{AB}} = \frac{{AE}}{{AC}} = \frac{{DE}}{{BC}}\)

\(\begin{array}{l} \frac{4}{{4 + 3}} = \frac{{DE}}{{BC}}\\ \frac{{DE}}{{BC}} = \frac{4}{7} \end{array}\)

Similarly in ΔDOE & ΔBOC

∠DEO = ∠OBC (Corresponding angles are equal)

∠DOE = ∠BOC (vertically opposite angles)

∴ ΔDEO ∼ ΔOBC

\(\begin{array}{l} \frac{{DE}}{{BC}} = \frac{{DO}}{{OC}}\\ \frac{{DO}}{{OC}} = \frac{4}{7} \end{array}\)

Hence, \(\frac{{DO}}{{DC}} = \frac{4}{{4 + 7}} = \frac{4}{{11}}\)