Hello, kohila!

Here is some help . . .

3. A circle is passing through three vertices of a rhombus of side 8cm

and its centre is the forth vertex of the rhombus.

Find the length of the longest diagonal of the rhombus.

We have rhombus .

The center of the circle is

Since , the rhombus

. . is made of two equilateral triangles.

Hence:

Law of Cosines: .Code:B * 8 * : * 8 * : * * : * A * * * * * * * * * C * : * * : * 8 * : * 8 * O

. . . . . . . . . . . .

Therefore: .

4. In a rhombus ABCD, the diagonals intersect each other at O.

If ∠ A = 60° and OA = 2 cm, find the length of a side of the rhombus.

Once again, the rhombus is comprised of two equilateral triangles.

The altitude of the equilateral triangle is 2.Code:B * * : * * : * * 2 : * A * - - - + - - - * C * :O * * : * 8 * : * 8 * D

Pythagorus: .Code:* *|* * | * x * |2 * * | * * | * * * * * * * * x/2

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