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EastWind [94]
2 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]2 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]2 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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<h3>Answer:   40</h3>

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

Explanation:

JQ is longer than QN. We can see this visually, but the rule for something like this is the segment from the vertex to the centroid is longer compared to the segment that spans from the centroid to the midpoint.

See the diagram below.

The ratio of these two lengths is 2:1, meaning that JQ is twice as long compared to QN. This is one property of the segments that form when we construct the centroid (recall that the centroid is the intersection of the medians)

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