Question 82527
the center of the circle lies on the line connecting the midpoints of the chords, this line is also perpendicular to the chords


let x equal the distance from the center to the 30 cm chord, so 23-x equals the distance to the 16 cm chord


a right triangle is formed by x, half of the 30 cm chord and the radius


similarly, another right triangle is formed by 23-x, half of the 16 cm chord and the radius


using Pythagoras, {{{x^2+15^2=r^2}}} and {{{(23-x)^2+8^2=r^2}}} ... so {{{x^2+225=529-46x+x^2+64}}} ... 225=593-46x ... x=8


{{{8^2+15^2=r^2}}} ... {{{289=r^2}}} ... r=17 cm