geometry

[Yashwanth]

the bisector of a in abc meets at u. if ux is drawn parallel to ac meeting ab at x, and y drawn parallel to ab meets ac at y , prove that bx/cy=ab^2//ac^2

 

[Deleted member 4993]

the bisector of a in abc meets at u. if ux is drawn parallel to ac meeting ab at x, and y drawn parallel to ab meets ac at y , prove that bx/cy=ab^2//ac^2

You write:

the bisector of a in abc meets at u.

Meets what at u? Can you please draw a sketch of the given problem?

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this assignment.

 

[Dr.Peterson]

the bisector of a in abc meets at u. if ux is drawn parallel to ac meeting ab at x, and y drawn parallel to ab meets ac at y , prove that bx/cy=ab^2//ac^2

I think you may mean this, where I have added many words, and used letters more carefully to distinguish lines from points:

Given a triangle ABC, the bisector of angle A intersects BC at U; the line through U parallel to AC intersects AB at X; and the line through U parallel to AB intersects AC at Y. Prove that BX/CY = AB^2/AC^2.​

Assuming that is correct, we need to know what help you need. Do you have some idea how to start? (That doesn't mean knowing the first steps of the proof; it just means seeing some possible things to do with the givens that might lead to something useful, such as identifying some similar triangles.)

Also, if this problem is in the context of a course, what topics have you learned recently that it might be intended to give you practice with? (For example, were you taught a theorem about angle bisectors in triangles?)