Question

3.[–/1 Points]DETAILSALEXGEOM7 6.3.007.MY NOTESASK YOUR TEACHERConsider the following theorem.If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.O is the center of the circle. A circle contains six labeled points and four line segments.•The center of the circle is point O.•Points A, B, C and D are on the circle. Point A is on the top middle, point B is on the bottom right, point C is slightly above the middle right, and point D is on the bottom left.•A line segment connects points A and B.•A line segment connects points C and D.•A line segment connects points A and D.•A line segment connects points C and B.•Point E is the intersection of line segments A B and C D. Point E is to the right and slightly below point O.Given:AE = 3EB = 2DE = 6Find:ECEC =

Answer 1

Given:

Find-:

Value of EC.

Explanation-:

Use the property then,

`AE* EB=DE* EC`

Put the value and solve for EC.

`\begin{gathered} 3*2=6* EC \\ \\ EC=(3*2)/(6) \\ \\ EC=1 \end{gathered}`

So, the value of EC is 1.