In a triangle ABC AB : AC = 5 : 2, BC = 9 cm. BA is produced to D, and the bisector of the Angle CAD meets BC produced at E. What is the length (in cm) of CE?
Answer & explanation
Correct answer: option 4
According to the question
\(\frac{AB}{AC}\) = \(\frac{BE}{CE}\) (Using external angle bisector theorem)
= \(\frac{5}{2}\) = \(\frac{9 + CE}{CE}\)
= 5CE = 18 + 2CE
= 3CE = 18
= CE = 6 cm
Therefore, CE is 6 cm.