Chapter 9.2, Problem 15PSB

To determine

To find:The value of chord CD

Answer to Problem 15PSB

The value of chord $CD=2.4$

Explanation of Solution

Given information:The following values are given

  $AB=4$

  $BE=5$

  $AE=6$

  $CE=3$

Formula used:If all the angles of any two triangles are given congruent, then the triangles are said to be similar. And similar triangles have sides in the same ratio.

Calculation:We know by AAA property, that the triangles AEB and DEC similar. Hence, the sides of these triangles will also be in the same ratio. Thus, we have

  $\frac{AB}{CD}=\frac{BE}{CE}$

Now, substituting the values of AB, BE, and CE we get

  $\frac{4}{CD}=\frac{5}{3}$

  $CD=2.4$