In trapezoid ABCD the bases of BC and AD are 8cm and 12cm diagonal AC

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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