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Question
In trapezium ABCD, side AB || side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15 then Find OD.
Solution
Given:
side AB || side DC
AB = 20,
DC = 6,
OB = 15
In △COD and △AOB
∠COD = ∠AOB (Vertically opposite angles)
∠CDO= ∠ABO (Alternate angles, CD || BA and BD is a transversal line)
By AA test of similarity
△COD ∼ △AOB
∴ `(CD)/(AB) = (OD)/(OB)` (Corresponding sides are proportional)
\[ \Rightarrow \frac{6}{20} = \frac{OD}{15}\]
\[ \Rightarrow OD = 4 . 5\]
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