Question

In the circle below, CD is a diameter. If AE=10, CE=4, and AB=16, what is

the length of the radius of the circle?
Please Help ASAP

Answer 1

the length of the radius of the circle is 7.5

How to determine the length of the radius of the circle

From the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

AE = 10, CE = 4, and AB=16

This means that

10 * (16 - 10) = 4 * DE

This gives

DE = 10 * (16 - 10)/4

Divide by 2 for the radius

DE/2 = 10 * (16 - 10)/8

Evaluate

DE/2 = 7.5

Hence, the length of the radius of the circle is 7.5

Answer 2

(D)9.5 Units

Explanation:

We have two chords CD and AB intersecting at E.

Using the theorem of intersecting chords

AE X EB =CE X ED

• AE=10
• CE=4
• AB=16

AB=AE+EB

16=10+EB

EB=16-10=6

Therefore:

AE X EB =CE X ED

10 X 6 = 4 X ED

ED =60/4 =15

Therefore:

CD=CE+ED

=4+15

CD=19

Recall that CD is a diameter of the circle and;

Radius =Diameter/2

Therefore, radius of the circle =19/2 =9.5 Units