The problem you provided is in Hebrew and involves geometric concepts related to a circle, angles, and areas of triangles. Here's a rough translation of the question:

Problem 4:

The points $A$, $B$, $C$, and $D$ lie on the circumference of a circle with radius $R$.
The diagonals of quadrilateral $ABCD$ intersect at point $E$.

Given:

• $\angle ACD = \alpha$
• $\angle ABC = \alpha$
• $AB = AC$
• $BD$ bisects $\angle ABC$

a. The area of triangle $\triangle ABE$ is 3 times larger than the area of triangle $\triangle CDE$.
Find $\alpha$.

b. Determine whether it is possible to inscribe a rhombus inside quadrilateral $ABCD$.

To proceed with solving this, let's break it down:

Part (a):

1. You're given that the areas of triangles $\triangle ABE$ and $\triangle CDE$ have a specific ratio. Using this information and the properties of the circle, we can apply geometric formulas for areas and angles.

2. You also know that $AB = AC$, meaning triangle $ABC$ is isosceles. This symmetry might help in setting up the angle relationships, particularly with $\angle ACD$ and $\angle ABC$ both being $\alpha$.

Part (b):

1. This asks whether a rhombus can be inscribed within the quadrilateral. Analyzing the side lengths and angle properties of quadrilateral $ABCD$ can help solve this.

Would you like me to work through the equations and provide the solution for $\alpha$ and the rhombus question?