Video Transcript
Given that 𝐸𝐶 equals four, 𝐸𝐷
equals 15, and 𝐸𝐵 equals six, find the length of the line segment 𝐸𝐴.
Let’s look at the diagram more
closely. We can see that it consists of a
circle, in which there are two intersecting chords. They’re the lines 𝐴𝐵 and
𝐶𝐷. We’ve also been given various
lengths that we can add to our diagram. The length of the line segment 𝐸𝐶
is four. The length of the line segment 𝐸𝐷
is 15. And the length of the line segment
𝐸𝐵 is six.
We’re asked to work out the length
of the line segment 𝐸𝐴. So we need to recall the
relationship that exists between the lengths of the line segments of intersecting
chords. We remember that “if two chords
intersect in a circle, then the products of the lengths of the chord segments are
equal.”
Our two chords intersect inside the
circle at the point 𝐸. So we have that the product of the
lengths of the chord segments of the orange chord, that’s 𝐸𝐴 multiplied by 𝐸𝐵,
is equal to the product of the length of the chord segment of the pink cord. That’s 𝐸𝐶 multiplied by 𝐸𝐷. We know the lengths of the chord
segments 𝐸𝐵, 𝐸𝐶, and 𝐸𝐷. So we can substitute their values
into this equation given that the length of the chord segment 𝐸𝐴 multiplied by six
is equal to four multiplied by 15.
Dividing both sides of this
equation through by six gives a calculation that we can use to find the length of
the chord segment 𝐸𝐴. It’s equal to four multiplied by 15
over six. Four multiplied by 15 is equal to
60. And 60 divided by six is equal to
10.
Using then the relationship between
the lengths of chord segments for chords which intersect inside a circle, we found
that the length of the chord segment 𝐸𝐴 is 10. There’re no units for this as there
were no units for the original measurements we were given for the other three chord
segments.
