Geometry Homework Help

Question

Image Link : http://imgur.com/a/WKrkH

Questions:

(1) What is the length of RS in circle O?
(2) What is the value of r to the nearest tenth?

Thank in advanced!

Answer 1

RS is the same perpendicular distance from the center as the other chord R_  (can see the point Q in the middle, but not the letter for the endpoint on the circle).  There is some Geometry Theorem somewhere that says when two chords are the same perpendicular distance from the center, then the chords are congruent.  So the chord R__ is 27 units long, so RS is also 27 units long.

 

Draw a line from "O" to "R".  This is the radius r, and it is the hypotenuse of a right triangle with horizontal leg 13.5 units long and vertical leg 8 units long.  a² + b² = c²  so  

 

13.5² + 8² = r²    r² = 246.25

square root both sides and get that r = 15.69235, to the nearest then r = 15.7 units.