Question

In the given figure, CD and AB are intersecting chords and EF is a tangent to the circle. If OD = 4 cm, OB = 12 cm, OA = 4 cm and DE = 4 cm, then the length of EF is equal to

• A.
  $10\sqrt{5}$
• B.
  $4\sqrt{5}$
• C.
  $2\sqrt{5}$
• D.
  $6\sqrt{5}$

Answer 1

The correct option is B

$4\sqrt{5}$
Given: OD = 4 cm, OB = 12 cm, OA = 4 cm, DE = 4 cm

Also, it is given that CD and AB are intersecting chords and EF is tangent to the circle.



AB and CD are the intersecting chords.

$\Rightarrow OC\times OD=OB\times OA\Rightarrow OC\times 4=12\times 4\Rightarrow OC=12cm$

Apply Tangent Secant Theorem
$\Rightarrow E{F}^2=ED\times EC\Rightarrow E{F}^2=4\times 20(\because EC=DE+OD+OC)\Rightarrow EF=4\sqrt{5}cm$

Thus, the length of EF is $4\sqrt{5}cm$

Hence, the correct answer is option b.