ABCD IS A RHOMBUS WITH A CIRCLE INSCRIBED IN IT TOUCHING ALL SIDES OF THE RHOMBUS.IF BCE IS AN EQUILATERAL TRIANGLE AND IF CE=4√ 3 CM.FIND THE RADIUS OF THE CIRCLE

Answer 1

For a rhombus with side s and (smaller ) interior angle θ, the radius of the inscribed circle can be worked out to be

r = (s/2) sin(θ) sqrt[1 +2 cos( θ) ]

Since you don't say where point E is located, I assume that what is intended is;

θ = 60 degrees and s = 4 sqrt(3)

Plugging in r = 3 sqrt(2)

The derivation of the formula for r involves noting that the center of the circle is at the intersection of the two diagonals of the rhombus and use of the law of cosines to find the length of the longer diagonal.

Answer 2

Is there some more information about the diagram? Where is point E in relation to the other points?