The chords AB and CD meet at point E. Find ED if: a). AE = 5 cm, BE = 2 cm, CE = 2.5 cm.
| August 22, 2021 | education
The chords AB and CD meet at point E. Find ED if: a). AE = 5 cm, BE = 2 cm, CE = 2.5 cm. B). AE = 16 cm, BE = 9 cm, CE = ED
Let us use the property of intersecting chords, according to which the product of the segments formed at the intersection of one chord is equal to the product of the lengths of the segments of the other chord.
AE * BE = CE * DE.
DE = AE * BE / CE = 5 * 2 / 2.5 = 10 / 2.5 = 4 cm.
Similarly for b).
AE * BE = CE * DE.
Since CE = DE, then AE * BE = CE2.
CE2 = 16 * 9 = 144.
DE = CE = 12 cm.
Answer: The lengths of the DE segments are equal: a) 4 cm, b) 12 cm.
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