In a trapezoid with bases AD and BC, the diagonals intersect at point O, BO: OD = 3: 2, AC = 25 cm. Find OC and AO.
| June 1, 2021 | education
In a trapezoid, the AOD and COB triangles are similar, so you can make the proportion:
BC: AD = BO: OD = OC: AO = 3: 2.
Now let OC = x, then AO = 25 – x, therefore:
OC: AO = x: (25 – x) = 3: 2,
2x = 75 – 3x,
x = 15.
Thus, we get that OS = 15 cm, AO = 25 – 15 = 10 cm.
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