Circle q (1 Viewer)

[chingyloke]

The diagram below shows the arc of a circle formed by chord (y). The line (x) is the perpendicular bisector of the chord y.


Show that the radius (r) of the circle is given by r=y^2/8x + x/2

can anyone help? muchly appreaciated. diagram is attached.

 

[lolokay]

hint: pythagoras.. (and circle geo properties)

 

[chingyloke]

ah i'm sort of getting close. anymore help?

 

[jet]

say you extend the line of length x to the other end of the circle. By one of the theorems, this passes through the centre of the circle (im assuming it bisects the chord aswell).
Then you use the intercept theorem. Let the length of the extended bit be z. Therefore
xz = (y/2)(y/2) = y²/4
Hence z = y²/4x
Therefore the diameter is equal to y²/4x + x
And the radius equals y²/8x + x/2

 

[chingyloke]

ahhhh. intercept theorem. thankyou so much.

circle geometry..grrr :mad1: