In trapezoid ABCD the bases of BC and AD are 8cm and 12cm diagonal AC is 40cm and crosses the diagonal BD at point O find the difference between AO and CO.
Triangles BOС and AOD are similar in two angles, the angle BOS = AOD as vertical angles, the angle OBC = ADO as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AB.
Let the length of the segment AO = X cm, then the length of the segment CO = (40 – X) cm.
Then in similar triangles ВOС and AOD:
BC / AD = CO / AO.
8/12 = (40 – X) / X.
8 * X = 12 * (40 – X).
12 * X + 8 * X = 480.
20 * X = 480.
X = AO = 480/20 = 24 cm.
Then CO = 40 – 24 = 16 cm.
AO – CO = 24 – 16 = 8 cm.
Answer: The difference between the AO and CO segments is 8 cm.
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