Question

ромб ABCD проведены диагонали AC и BD угол ABD 60 градусов CD 13 см найти АО О точка пересечения диагоналей ​

Answer 1

Ответ:

СД=13

АО=СО

СО=СД÷2

СО=6.5

АО=6.5

Объяснение:

вроде бы так

Answer 2

Problem Analysis

We are given a rhombus ABCD with diagonals AC and BD intersecting at point O. The angle ABD is given as 60 degrees and CD is given as 13 cm. We need to find the length of AO.

Solution

To find the length of AO, we can use the properties of a rhombus and the given information.

1. In a rhombus, the diagonals bisect each other at right angles. Therefore, angle AOB is also 60 degrees.

2. Since angle AOB is 60 degrees, triangle AOB is an equilateral triangle. In an equilateral triangle, all sides are equal.

3. Let's assume the length of AO as x. Since triangle AOB is equilateral, the length of BO is also x.

4. In triangle AOB, we have two sides equal, AO = BO = x, and the angle AOB is 60 degrees. We can use the cosine rule to find the length of AB.

Cosine Rule: c^2 = a^2 + b^2 - 2ab * cos(C)

In triangle AOB, a = AO = x, b = BO = x, and angle AOB = 60 degrees.

Plugging in the values, we get: AB^2 = x^2 + x^2 - 2(x)(x) * cos(60) AB^2 = 2x^2 - 2(x^2)(0.5) AB^2 = 2x^2 - x^2 AB^2 = x^2

Therefore, AB = x.

5. Now, we can use the Pythagorean theorem in triangle AOB to find the length of OB.

Pythagorean Theorem: c^2 = a^2 + b^2

In triangle AOB, a = AO = x, b = AB = x, and c = OB.

Plugging in the values, we get: OB^2 = x^2 + x^2 OB^2 = 2x^2

Therefore, OB = sqrt(2x^2) = sqrt(2) * x.

6. Now, we can use the Pythagorean theorem in triangle OCB to find the length of CB.

In triangle OCB, a = OB = sqrt(2) * x, b = CD = 13 cm, and c = CB.

Plugging in the values, we get: CB^2 = (sqrt(2) * x)^2 + 13^2 CB^2 = 2x^2 + 169

Therefore, CB = sqrt(2x^2 + 169).

7. Since CB is a side of the rhombus, it is equal to AB. Therefore, we can equate the expressions for CB and AB.

sqrt(2x^2 + 169) = x

Squaring both sides, we get: 2x^2 + 169 = x^2

Simplifying, we get: x^2 = 169 x = sqrt(169) x = 13

8. Therefore, the length of AO is 13 cm.

Answer

The length of AO is 13 cm.

Explanation

We can find the length of AO by using the properties of a rhombus and the given information. Since triangle AOB is an equilateral triangle, the length of AO is equal to the length of AB. By equating the expressions for CB and AB, we can solve for the length of AO, which is found to be 13 cm.