Question

In the given figure $AC,CE$ and $EH$ are tangents drawn to the circle at $B,D$ and $F$ respectively. If $CB=5cm$ and $EF=3cm$, then length of $CE$ is

• A. $2cm$
• B. $5cm$
• C. $3cm$
• D. $8cm$

Answer 1

The correct option is D $8cm$

Given, $CB=5cm$ and $EF=3cm$

Tangents $AC$ and $CE$ passes through $B$ and $D$ respectively and intersect at point $C$.

As they intersect and passes through different point on the circle, so the length of tangents from the point on circle and intersecting point is same.

$\therefore$ length of $CD=$ length of $CB$

$\therefore$ $CD=5cm$

Similarly, length of $DE=$ length of $EF$

$\therefore$ $DE=3cm$.

Also, $CE=CD+DE=5+3=8cm$.

$\therefore$ $CE=8cm$.

Hence, option D is correct.