# Circumscribable Quadrilateral and Finding Lengths

In the attached figure, the quadrilateral ABCD has the following lengths of sides and diagonals: DC=7, CB=8, BA=13, AD=13, AC=15, and BD=13.

1. Verify that quadrilateral ABCD is circumscribable

2. Find the remaining lengths of DE, BE, AE, and CE.

Although it appears there is a right angle, it is not labeled as though it is, so treat it like there is not a right angle.

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In the attached figure, the quadrilateral ABCD has the following lengths of sides and diagonals: DC=7, CB=8, BA=13, AD=13, AC=15, and BD=13.

(1). Verify that quadrilateral ABCD is circumscribable

We will prove that the quadrilateral ABCD is NOT circumscribable. Suppose that quadrilateral ABCD is circumscribable. Then we can find the area of the quadrilateral ABCD, say A, which is the sum of the areas of two triangles and .

Since is an equilateral triangle, the area is . By part (2), we know that . So,

. So, the area ...

#### Solution Summary

This comprehensive, well explained solution includes a diagram. Circumscibability is investigated and the lengths are found.