Question

В окружности с центром в точке О проведены диаметры AC и BD. Найдите хорду AD, если AB=7 см, CB=9 см. Срочно нужно.

Answer 1

В четырёхугольнике ABCD диагонали AB и CD точкой пересечения O делятся пополам, следовательно он параллелограмм, тогда AD=CB=9см

Answer 2

Solution:

Given that AB = 7 cm and CB = 9 cm, we can find the length of the chord AD in the circle with center O.

First, let's find the length of AC and BD using the given information.

We have the following information from the search results: - AC = AD - BD = AB

Now, we can use the Pythagorean theorem to find the length of AC and BD.

Using the Pythagorean theorem: AC^2 = AO^2 + OC^2 BD^2 = BO^2 + OD^2

Since AC = AD and BD = AB, we can substitute these values and solve for the lengths.

Calculation:

AC^2 = AO^2 + OC^2 BD^2 = BO^2 + OD^2

Now, let's find the lengths of AC and BD using the given information.

AC^2 = AO^2 + OC^2 AC^2 = (AB/2)^2 + BC^2 AC^2 = (7/2)^2 + 9^2 AC^2 = 49/4 + 81 AC^2 = 49/4 + 324/4 AC^2 = 373/4

BD^2 = BO^2 + OD^2 BD^2 = (CB/2)^2 + BC^2 BD^2 = (9/2)^2 + 7^2 BD^2 = 81/4 + 49 BD^2 = 81/4 + 196/4 BD^2 = 277/4

Now, we have the squares of the lengths of AC and BD. To find the actual lengths, we take the square root of these values.

AC = √(373/4) BD = √(277/4)

AC ≈ 9.67 cm BD ≈ 8.33 cm

So, the length of the chord AD is approximately 9.67 cm.

This calculation is based on the given information and the application of the Pythagorean theorem to find the lengths of AC and BD.