Question

Ребяят,помогите даю 40 БАЛЛОВ!!(Знаю много,но я хочу удостовериться в ответе).В трапеции ABCD основание AD=20 см,BC=15. Диагональ AC= 35 см.О-точка пересечения диагоналей. Определите OC??

Answer 1

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Answer 2

Calculation of OC in Trapezoid ABCD

To determine the length of OC in trapezoid ABCD, we can use the properties of diagonals in a trapezoid.

Given information: - Base AD = 20 cm - Base BC = 15 cm - Diagonal AC = 35 cm

To find OC, we need to find the length of OD and subtract it from the length of AC.

To find OD, we can use the fact that the diagonals of a trapezoid divide each other proportionally. This means that the ratio of the lengths of the segments formed by the point of intersection O is equal to the ratio of the lengths of the bases.

Let's denote the length of OD as x. Then, the length of OC can be calculated as follows:

OC = AC - OD

To find x, we can set up a proportion using the lengths of the bases:

AD/BC = OD/OC

Substituting the given values:

20/15 = x/OC

Simplifying the equation:

4/3 = x/OC

Cross-multiplying:

4 * OC = 3 * x

Solving for x:

x = (4/3) * OC

Substituting this value back into the equation for OC:

OC = AC - (4/3) * OC

Simplifying the equation:

(7/3) * OC = AC

Solving for OC:

OC = AC * (3/7)

Now, let's substitute the given value of AC = 35 cm into the equation:

OC = 35 * (3/7)

Calculating the value of OC:

OC = 15 cm

Therefore, the length of OC in trapezoid ABCD is 15 cm.

Answer:

The length of OC in trapezoid ABCD is 15 cm.