In the figure below two chords xy and yz are 150 ft each and

In the figure below, two chords (xy and yz) are 150 ft each, and the perpendicular distance yw is 15 ft. Determine the radius of the curve. (cos2x=cos²x-sin²x=1-2sin²x)

Solution

Triangle formed by chords xy and yz form two rt angled triangles:xyw and yzw

length of xw = sqrt(150^2 - 15^2) = 149.25 ft

Solve for the radius, R, using the Pythagorean theorem, knowing the length of xw and wz:

xc = R ; wc = R-15 ;

xc^2 = xw^2 +wc^2

R^2 = (149.25)^2 +(R-15)^2

30R = 22500

R = 750 ft