Question

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 from that line by the legs of the trapezoid. Plz explain thx

Answer 1

Answer:

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

Since triangles BOC and AOD are somilar, then

[tex] \dfrac{AO}{OC}=\dfrac{DO}{OB}=\dfrac{AD}{BC}=\dfrac{b}{a}. [\tex]

OC/AO = OB/DO = BC/AD=/ba

Triangles OAE and CAB are similar

EO/BC=b/(a+b)

EO=ab/(a+b)

again

OF=ba/(b+a)

and.

EF=2a/(a+b) is arequired length.

Answer 2

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