Two equal chords AB and CD meet at point E. Calculate the length of the chord, if AE is 3cm, DE is 2cm
| December 13, 2020 | education
The chords are equal, i.e. AB = CD
AB = AE + EB
CD = CE + ED
Subtract one from the other and get 1 + EB = CE
There is a formula for the case of intersection of chords
In our case, it looks like this:
AE * EB = CE * ED
Substituting 1 + EB = CE and the data in the value conditions, we get
3 * EB = 2 + 2 * EB, whence EB = 2, CE = 3, therefore both chords are 5 cm
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