Given: Concentric circles with center O; AB= 18: BE=4; CO―perpAB― Find: EO

Expert Answer to "Given: Concentric circles with center O; AB= 18:..."

defazajx

2021-08-09

Given: Concentric circles with center O; AB= 18: BE=4;

\overset{―}{C O} p e r p \overset{―}{A B}

Find: EO

gotovub

Skilled2021-08-10Added 98 answers

solution below

Vasquez

Expert2021-12-24Added 669 answers

Step 1

From the figure, we see that EO and CO are radius

Let EO=CO=r

So, BO=EO+BE=r+4

We have AB=18

So, $B C = \frac{18}{2} = 9$

Step 2

Triangle OBS is a right triangle.

We use the Pythagorean identity for it

$O C^{2} + B C^{2} = O B^{2}$

$r^{2} + 9^{2} = (r + 4)^{2}$

$r^{2} + 81 = r^{2} + 8 r + 16$

81=8r+16

8r=81-16

8r=65

$r = \frac{65}{8}$

r=8.125

Answer: EO=8.125

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