In ΔABC, AB = 7 cm, BC = 10 cm, and AC = 8 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then DC (in cm) = ?
Answer & explanation
Correct answer: option 2
As we know,
If AD bisect \(\angle\)BAC, then,
⇒ \(\frac{AB}{AC}\) = \(\frac{BD}{DC}\)
⇒ \(\frac{7}{8}\) = \(\frac{BD}{DC}\)
⇒ DC = \(\frac{8BD}{7}\) ..(1.)
⇒ BD + DC = BC
⇒ BD + \(\frac{8BD}{7}\) = 10
⇒ \(\frac{15BD}{7}\) = 10
⇒ BD = 10 x \(\frac{7}{15}\)
⇒ BD = \(\frac{14}{3}\)
Putting in equation (1.)
⇒ DC = \(\frac{14}{3}\) x \(\frac{8}{7}\)
⇒ DC = \(\frac{16}{3}\)