# URGENT NEED OF HELP

#### mira222

##### New member
Two circles meet at A and B. A chord CD of one circle is produced to meet the other circle at E and F so that CDEF is a straight line, as shown. The common chord AB is produced to meet the line CF at a point M between D and E. If M is the midpoint of CF and angle CAF=90 degrees, prove that AC//BD and AF//BE are parallel.

#### Subhotosh Khan

##### Super Moderator
Staff member
Two circles meet at A and B. A chord CD of one circle is produced to meet the other circle at E and F so that CDEF is a straight line, as shown. The common chord AB is produced to meet the line CF at a point M between D and E. If M is the midpoint of CF and angle CAF=90 degrees, prove that AC//BD and AF//BE are parallel.
Hint: Draw a sketch of the "situation" as described.

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#### mira222

##### New member
Two circles meet at A and B. A chord CD of one circle is produced to meet the other circle at E and F so that CDEF is a straight line, as shown. The common chord AB is produced to meet the line CF at a point M between D and E. If M is the midpoint of CF and angle CAF=90 degrees, prove that AC//BD and AF//BE are parallel.

#### Subhotosh Khan

##### Super Moderator
Staff member
Two circles meet at A and B. A chord CD of one circle is produced to meet the other circle at E and F so that CDEF is a straight line, as shown. The common chord AB is produced to meet the line CF at a point M between D and E. If M is the midpoint of CF and angle CAF=90 degrees, prove that AC//BD and AF//BE are parallel.
What have you been taught about lengths of intersecting chords of circles?

#### mira222

##### New member
I have only learn basic geometry, but please I am very confused on this problem

#### Subhotosh Khan

##### Super Moderator
Staff member
I have only learn basic geometry, but please I am very confused on this problem
Please do a google search with keywords - "intersecting chords of circles" - and tell us what you found?

#### Dr.Peterson

##### Elite Member
I have only learn basic geometry, but please I am very confused on this problem
If this problem was assigned in your course, then there is probably a method to solve it within that course. What have you learned in the course? That will help us think of alternative ideas.

If it is outside of a course (e.g. a contest problem or an admission test), then it tells you that you need to learn more geometry in order to do what is expected. Can you tell us about the context (as we ask you to do)?

Now, I think I already told someone else what I would do with this same problem. Draw in segments CA and AF, and think about the fact that CAF is a right triangle. Then the facts about intersecting chords or secants can be used; or perhaps something else that you have learned could take the place of those theorems. (But the theorems are very much worth learning!)

#### riteshkumarmanjwani

##### New member
Two circles meet at A and B. A chord CD of one circle is produced to meet the other circle at E and F so that CDEF is a straight line, as shown. The common chord AB is produced to meet the line CF at a point M between D and E. If M is the midpoint of CF and angle CAF=90 degrees, prove that AC//BD and AF//BE are parallel.
I got the solution
You can use Intersecting Secant Theorem