Question

AE is the bisector of exterior $\angle CAD$ meeting BC produced in E. If AB = 10 cm, AC = 6 cm and CE = 18 cm, then find BC.

• A.
  12 cm
• B.
  13 m
• C.
  14 cm
• D.
  18 cm

Answer 1

The correct option is A

12 cm
AE is bisector of exterior $\angle CAD$ meeting BC produced in E.

By exterior angle bisector theorem,




$\frac{AB}{AC}=\frac{BE}{CE}\Rightarrow \frac{10}{6}=\frac{BC+CE}{CE}\Rightarrow \frac{5}{3}=\frac{BC+18}{18}\Rightarrow 5\times 18=3(BC+18)\Rightarrow 90=3BC+54\Rightarrow 90-54=3BC\Rightarrow 36=3BC\Rightarrow \frac{36}{3}=BC\therefore BC=12cm$

Hence, option a is correct.