Question

In trapezlum ABCD, (Figure 1.60) side AB || side
DC, diagonals AC and BD intersect in point O. If
AB= 20, DC-6, OB = 15 then find OD.
0
B В
A
none
4.5
45
5.4​

Answer 1

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In the given figure,

AB || CD is given to us,

AB = 20

DC = 6

OB = 15

Now,

In triangle COD and triangle AOB,

∠DCO = ∠OAB (alternate interior angles)

∠CDO = ∠OBA (alternate interior angles)

and,

∠COD = ∠AOB (vertically opposite angles)

So,

ΔCOD ≈ ΔAOB (By, AAA similarity)

Now,

From CPCT we can say that,

0D/OB = CD/AB

So,

OD/15 = 6/20

So,

OD = 6 × 15/20

OD = 9/2

OD = 4.5

Therefore the length of the side OD is 4.5.