All sides of quadrilateral ABCD are tangent to circle P. What is the perimeter of quadrilateral ABCD?

Given:

Let us assume that E,F,G,H be the points at which the circle touches the line segment AB, BC, CD, DA.

The length of EB = 9.6 units.

The length of AH = 3.7 units.

The length of CD = 12 units.

We need to determine the perimeter of ABCD.

Lengths of sides of the quadrilateral ABCD:

Let CG = x, then DG = 12 - x

We know the property the property that "if the lengths of the two tangents drawn from an exterior point to a circle are equal".

Hence, applying the property, we have;

AH = AE = 3.7 units.

EB = BF = 9.6 units.

CG = CF = x units.

DG = DH = (12 - x) units.

Perimeter of quadrilateral ABCD:

The perimeter of ABCD can be determined by adding all the lengths of the sides of the quadrilateral ABCD.

Thus, we have;

Substituting the values, we have;

Thus, the perimeter of the quadrilateral ABCD is 50.6 units.

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