Answer:
DE = 29.57
Step-by-step explanation:
Given:
AX = 15 cm,
CX = 12 cm,
EX = 21 cm.
Required:
Find DE
Solution:
AX and CX are segments of chord AC
DX and EX are segments of chord DE
Therefore,
DE = DX + EX
DE = DX + 21
We are not given the value of DX, so we need to find DX
Based on the intersecting chords theorem:
AX*CX = DX*EX
Plug in the values
15*12 = DX*21
180 = DX*21
Divide both sides by 21
180/21 = DX
8.57142857 = DX
DX ≈ 8.57
✅DE = DX + 21 = 8.57 + 21 = 29.57
