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

is should be y = 5x

step-by-step explanation:

correct me if im wrong

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584