Question

In the given figure, AB = 3 cm, DE = 5 cm. If AD = 4 cm, then BC is equal to

• A.
  $\frac{10}{3}cm$
• B.
  $9cm$
• C.
  $10cm$
• D.
  $\frac{16}{3}cm$
  

Answer 1

The correct option is B

$9cm$
Given: AB = 3 cm, DE = 5 cm, AD = 4 cm




Apply Secant Theorem

$\therefore AB\times AC=AD\times AE\Rightarrow AB\times (AB+BC)=AD\times (AD+DE)\Rightarrow 3\times (3+BC)=4\times (4+5)\Rightarrow 3+BC=\frac{4\times 9}{3}=12\Rightarrow BC=12-3=9cm$


Hence, the correct answer is option b.