Two chords, AC and DE, intersect inside of circle O at point X. AX=15 cm, CX= 12 cm, and EX= 21 cm. Find DE

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

yes

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