In ΔABC, BD is the internal bisector of ∠B meeting AC at D. If CD = 7 cm and AC = 10.5 cm, then AB : BC is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 2
By the angle bisector theorem, the bisector of an angle of a triangle divides the opposite side in the ratio of the other two sides: \(\displaystyle\frac{AB}{BC}=\frac{AD}{DC}\). So the two parts of AC give the ratio at once.
D lies on AC, so the part AD is \(AC-CD=10.5-7=3.5\) cm
Then \(AB:BC=AD:DC=3.5:7=1:2\)
