Question

If AK= 14, EK=17, BK= 7 , What is the length of DK? 12.7 8.5 7.0 3.5

Answer 1

Answer: the correct option is (B) 8.5.

Step-by-step explanation: Given that AK= 14, EK=17 and BK= 7 in the figure shown.

We are to find the length of DK.

From the figure, we note that

AD and BE are two chords of a circle intersecting at the point K.

We will be using the following theorem :

Intersecting Chord Theorem : When two chords intersect each other inside a circle, then the products of their segments are equal.

Applying the above theorem in the given circle, we get

`AK* DK=BK* EK\\\\\\\Rightarrow DK=(BK* EK)/(AK)\\\\\\\Rightarrow DK=(7* 17)/(14)\\\\\\\Rightarrow DK=(17)/(2)\\\\\Rightarrow DK=8.5.`

Thus, the length of DK is 8.5 units.

Option (B) is CORRECT.

Answer 2

To get the value of DK we use proportionality:
AK/EK=BK/KD
thus plugging the values we get:
14/17=7/KD
getting the reciprocal of getting both sides we have:

17/14=KD/7
thus
KD=17/14×7
KD=8.5
thus