QR Chord Question Help!

[ineffable11]

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I need help on TS test 1 QR #24.

Q: Chords AB and CD of circle O intersects at E.
AE=4
AB=5
CE=2
What is ED?

A: 2

Can anyone explain? I can't even draw the chords correctly.
Thanks!

 

[osimsDDS]

I need help on TS test 1 QR #24.

Q: Chords AB and CD of circle O intersects at E.
AE=4
AB=5
CE=2
What is ED?

A: 2

Can anyone explain? I can't even draw the chords correctly.
Thanks!

Draw a circle....then draw an X (like 2 diameter lines going from one side to another crossing in the middle somewhere) Then mark each AE is from one end to the middle...then AB is the whole diameter so you have to subtract 5-4=1 for EB. Then CE is 2 and ED=x

To find lengths of a chord use this formula:
(AE)(EB)=(CE)(ED)
(4)(1)=(2)(x)
x=4/2
x=2

 

[ineffable11]

You are so smart! I just didn't know how to draw X.. I literally wrote X on the edge of the circle. No wonder why the problem wasn't going anywhere. I guess too much DAT studying is making me lose my COMMON sense..
Thanks!!!😀

 

[drgreen]

To find lengths of a chord use this formula:
(AE)(EB)=(CE)(ED)

Can you please explain why this is the case, or how u derived this equation?

 

[klutzy1987]

The rule by all chords is that when one splits the other the product of the two parts of one chord is equal to the two parts of the other chord. I believe it is a postulate from 11th grade math.

 

[Streetwolf]

If you examine the chords and the triangles you can make from them, you find that the two triangles are congruent, which means their sides are proportional. From there you rearrange a bit to get that equation.