If AK= 14, EK=17, BK= 7 , What is the length of DK? 12.7 8.5 7.0 3.5
2 answers:
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
Thus, the length of DK is 8.5 units.
Option (B) is CORRECT.
You might be interested in
<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)
We know that JN = 60
Let x = JQ and y = QN
The ratio of x to y is x/y and this is 2/1
x/y = 2/1
1*x = y*2
x = 2y
Now use the segment addition postulate
JQ + QN = JN
x + y = 60
2y + y = 60
3y = 60
y = 60/3
y = 20
QN = 20
JQ = 2*y = 2*QN = 2*20 = 40
--------------
We have
JQ = 40 and QN = 20
We see that JQ is twice as larger as QN and that JQ + QN is equal to 60.