Question

in the circle below, chords AB and CD intersect at E. Determine BE.

Answer 1

im not sure how to solve this. someone walk me through please :*

Answer 2

i determined that side AC is 20.59 and AD is 20.12 does that make a difference?

Answer 3

is AB the diameter of the circle

Answer 4

yes AB is the diameter.

Answer 5

then angle ACB is 90
so AC^2 + BC^2 = AB^2 --eq1
BC^2 = CE^2 + BE^2
putting the value of BC^2 IN eq1,
AC^2 + CE^2 + BE^2 = (AE + BE)^2

now AC^2 = CE^2 + BE^2 --eq2

so,

putting the value of AC^2 IN --eq2

2*CE^2 + 2*BE^2 = (18 + BE)^2
2*100 + 2*BE^2 = (18 + BE)^2 -- eq3

SO we get a quadratic eq. in terms of BE

similarly we can get another eq in terms of BEfor the other side..
solving both the eq. simultaneously will yield the value of BE

Answer 6

sorry open study cut off on me. so BE is an equation not a number?

Answer 7

@sourav_aich

Answer 8

yes

Answer 9

and that equation is (18+BE)^2 ?

Answer 10

@sourav_aich

Answer 11

expand it and rearrange the terms to get a quadratic equation in terms of BE

Answer 12

okay what should the answer be? ill compare it to what i have.

Answer 13

i think BE = 39.19

Answer 14

@clynnew

Answer 15

okay im finishing up the work but it looks like thats what im going to get as well

Answer 16

yes

Answer 17

okay thats what i got as well

Answer 18

good