In a circle, chords AB and CD intersect each other at E. If CD = 18 cm, DE = 6 cm and AE = 18 cm, then BE = ?

It is given that,

The chord of the circle $$CD=8cm$$
$$DE=6cm$$
$$AE=18cm$$
$$BE=?$$

We know that intersecting chord theorem says that when two chord intersect each other in a circle then product of segments are equal.

Hence,$$AE \times EB=CE \times ED$$

Now, substituting the the values

$$\Rightarrow 18\times EB=(CE-ED)\times ED$$

$$\Rightarrow 18\times EB=(18-6)\times 6$$

$$\Rightarrow EB=\dfrac{12}{18}\times 6$$

$$\Rightarrow EB=4$$cm