In a trapezoid with bases of lengths a and b, a line parallel to the bases is drawn through the intersection point of the diagonals. Find the length of the segment that is cut f…

Question

asked Jun 9, 2020 120k views

1 Answer

Nicost · Answer 1 · 2020-06-14T22:52:16+0000

Answer:

(2ab)/(a+b).

Explanation:

Consider the trapezoid ABCD. In this trapezoid BC=a and AD=b.

Since triangles BOC and AOD are somilar, then

(AO)/(OC)=(DO)/(OB)=(AD)/(BC)=(b)/(a).

Triangles OAE and CAB are similar, then

$(EO)/(BC)=\dfar{AO}{AC}=(b)/(a+b).$

This means that

EO=(ba)/(b+a).

Similarly, from similar triangles FDO and CDB:

OF=(ba)/(b+a).

Thus,

EF=(2ab)/(a+b).