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In the figure at left, point C is the center of the circle. Line segment CDis perpendicular to line segment AB and bisects AB at the point E. It is known that AB and CD have length 10. What is the length of CE?

 

 Mar 16, 2021
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First we can draw AC to create right triangle ACE

 

Since AB = 10 and CD bisects AB at the point E, we can see that AE = 5

 

Since CD = 10 the radius of the circle is 10, which means AC = 10

 

Now we have a right triangle where two of the sides are known.

 

We can use the Pythagorean theorem to find the length of the unknown side.

 

AE2 + CE2  =  AC2

 

52  +  CE2   =   102

 

CE2   =   102  -  52

 

CE2   =   100 - 25

 

CE2   =   75

 

CE   =   √[ 75 ]

 

CE   =   5√3

 Mar 16, 2021

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