In the diagram below of circle o, chords AB and CD intersect at E.
1 answer:
Answer:
The length of EB is found 15
Step-by-step explanation:
As the diagram of the circle is not given in the question, I've found the diagram of the same question from internet and attached below. So that we can have a better understanding)
We can see in the diagram the chord AB and chord CD intersect each other at point E.
Each of the chord is divided into two segments.
According to the Intersecting Chords Theorem:
Products of the lengths of line segments on each chord are equal
Which means that
(AE)(EB) = (CE)(ED)
Substitute the given values;
(4)(EB) = (10)(6)
4(EB) = 60
EB = 15
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Alrighty
remember
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and
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for all real values of x
so
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which simplifies to
1=x²+4x-5
minus 1 both sides
0=x²+4x-6
use quadratic formula or complete the square
and 
2 solutions
remember
and
and
so
1=x²+4x-5
minus 1 both sides
0=x²+4x-6
use quadratic formula or complete the square
2 solutions