Two parallel chords of length 20cm and 11cm lie on opposite sides of a circle. The distance between the two chords is 15cm. Calculate, correct to the nearest whole number the radius of the circle
make a sketch
draw the radii to the end of each of the chords and complete the right-angled triangle.
let the distance from the centre to the longer chord be x, then the distance from the centre to the shorter chord is 15-x
Use Pythagoras in each of the triangles:
r^2 = x^2 + 10^2
and
r^2 = (15-x)^2 + (11/2)^2
so
100 = 121/4 + 225 - 30x
30x = 621/4
x = 207/40 = 5.175 cm
we have an equation for r^2 = ..
carry on