# Circumscribable Quadrilateral and Finding Lengths

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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

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

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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 ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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