Question

In the given figure, the measurements indicated are in centimeter and $BC=10cm$. Find the length of BE.

• A. 30 cm
• B. 40 cm
• C. 50 cm
• D. 60 cm

Answer 1

Answer: (C)

50 cm

In triangle $ABC,AE$ is the external bisector of $\angle A$ and $AE$ cut the base $BC$ at point $E$.

We know that the external bisector will bisect the base into same ratio as the other two sides of triangle

$\therefore \frac{BE}{CE}=\frac{AB}{AC}$

$\Rightarrow \frac{10+CE}{CE}=\frac{15}{12}$

$\Rightarrow \frac{10}{CE}+1=\frac{15}{12}$

$\Rightarrow \frac{10}{CE}=\frac{3}{12}$

$\Rightarrow CE=40$cm

$\therefore BE=BC+CE=10+40=50cm$