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Find the radius of the circle in the diagram.

 

 Jan 3, 2020
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From center "O" draw a radius to either endpoint of the chord.

This radius will be length "R".   

 

From center "O" complete the radius to the intersection point of the two straight lines. 

This segment of the radius will be length "R" – 8.  


You have just created a right triangle. 

 

Use Pythagoras' Theorem                               R2  =  (R – 8)2 + 502    

Multiply it out                                                    R2  =  R2 –16R + 64 + 2500     

Subtract R2 from both sides                               0  =  –16R + 64 +2500

Add 16R to both sides                                    16R  =  64 + 2500

Add the constants                                           16R  =  2564

Divide both sides by 16                                       R  =  160.25

 Jan 4, 2020

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