Chords ac and bd intersect at e, with bd = 7 units, de = 2 units, and ae = 4 units. what is the length segment of ce

The length segment of ce is 2.5 units.



very to draw some sort of rough sketch. attached to this answer is a sketch of the circle with the current information.  the scale doesn't matter too much.

we use the intersecting chord theorem. according to this theorem, this equation is true:

    ae  · ce = be  · de

we are given that 

    bd = 7
    de = 2
    ae = 4

note that the theorem does not use bd. but bd is the length of an entire chord, and de is a portion of that chord. if we subtract de from bd, we should get be (the diagram to visualize):

    be = bd - de 
    be = 7 - 2 = 5

if we use the theorem and solve for ce, we get

    ce = be  · de / ae

using our information

    ce = 5  · 2 / 4
    ce = 2.5