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EastWind [94]
3 years ago
12

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

Mathematics
2 answers:
Elden [556K]3 years ago
8 0
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 
Doss [256]3 years ago
7 0

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 :

<u><em>Intersecting Chord Theorem :</em></u> 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\times DK=BK\times EK\\\\\\\Rightarrow DK=\dfrac{BK\times EK}{AK}\\\\\\\Rightarrow DK=\dfrac{7\times 17}{14}\\\\\\\Rightarrow DK=\dfrac{17}{2}\\\\\Rightarrow DK=8.5.

Thus, the length of DK is 8.5 units.

Option (B) is CORRECT.

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3 0
3 years ago
What is the area of this polygon?
Dennis_Churaev [7]

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4 0
3 years ago
The question is............
irina1246 [14]
A(n,s)=(ns^2)/(4tan(180/n)), n=number of sides, s=side length

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7 0
3 years ago
Could you please answer Number 2? This is for geometry
katrin [286]
Answer: 108 degrees

============================================================

Explanation:

Angle ABC is given to be 90 degrees. By the converse of Thales Theorem, we know that AC is a diameter of the circle. 
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Therefore, arc AC is 180 degrees as this is half the distance around the circle.

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7 0
3 years ago
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