In the diagram...

Question

In the diagram, diameter  intersects chord  at point E such that AE = 2.5 units and DE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. What is the approximate length of ?

A. 

5.5 units 

B. 

4.5 units

C. 

6.0 units

D. 

5.0 units

Answer 1

By Theorem for intersecting Chords:

AE * EC = DE * EB

AE is given as 2.5 and DE is given as 3.4.

We need to find EC.

EC = EO + OC

Since OC is the radius of the circle, it is 5.

AO is also the radius of the circle so it is equal to 5.

AO = AE + EO

5 = 2.5 + EO

EO = 2.5

EC = 5 + 2.5 = 7.5

So

AE * EC = DE * EB

2.5 * 7.5 = 3.4 * EB

EB = 5.5 (A)