In ΔABC, AD bisects ∠A and intersects BC at D. If BC = 5, AB = 4, AC = 8, then BD = ?
Answer & explanation
Correct answer: option 3
\(\frac{BD}{DC}\) = \(\frac{4}{8}\) [interior angle bisector theorem, AD cuts the opposite sides in the ratio of remaining sides]
BD = 4R , DC = 8R, therefore BC = 12R
BC =12R= 5 (given)
1R = \(\frac{5}{12}\)
BD = \(\frac{5}{12}\) × 4 = \(\frac{5}{3}\)