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AB and CD are two chords of a circle intersecting at the [#permalink]
02 Dec 2005, 11:50

AB and CD are two chords of a circle intersecting at the point E outside the circle so that
B and D are closer to E. If BE = 3 inches, AB = 5 inches, and ED = 4 inches, what is the
length of CD in inches?
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8

if you're interested in btw, hadzamir, i find your geo problems very interesting. Can you let me know the source or post more here?!! Thanks

one thing in your prove that i don't get:
why do you assume that ab and cd intersect in point O which is the center of the circle, or in other word - why do you assume that angle DOA is 180 degrees (why AD is a straight line?) same with line CB of course.

if you're interested in btw, hadzamir, i find your geo problems very interesting. Can you let me know the source or post more here?!! Thanks

one thing in your prove that i don't get: why do you assume that ab and cd intersect in point O which is the center of the circle, or in other word - why do you assume that angle DOA is 180 degrees (why AD is a straight line?) same with line CB of course.

Did i say so?! ..You should look more carefully at my illustration
The first part i was trying to prove that every angle form by two ends of a cord and a certain point in the circle is always = 1/2 angle formed by that cord's ends and the circle's centre ( This is a basic principle of geometry)
Then, i apply this rule to get DAB = DCB , COZ they're both =1/2 DOC ( YOU have to imagine this centre on your own, i don't put it in my illustration)

Again, there's nothing related to O in the second figure.

if you're interested in btw, hadzamir, i find your geo problems very interesting. Can you let me know the source or post more here?!! Thanks

one thing in your prove that i don't get: why do you assume that ab and cd intersect in point O which is the center of the circle, or in other word - why do you assume that angle DOA is 180 degrees (why AD is a straight line?) same with line CB of course.

Did i say so?! ..You should look more carefully at my illustration The first part i was trying to prove that every angle form by two ends of a cord and a certain point in the circle is always = 1/2 angle formed by that cord's ends and the circle's centre ( This is a basic principle of geometry) Then, i apply this rule to get DAB = DCB , COZ they're both =1/2 DOC ( YOU have to imagine this centre on your own, i don't put it in my illustration)

Again, there's nothing related to O in the second figure.

your geo problems are very interesting!! Can you please tell me the source or post more of them?! Thank you.

they are not from a book. i got them from a friend of mine (the paper called "hard questions"), but the real hard questions i have published here and i will continue to publish if i'll encounter with more.