Question

AB and CD are two parallel chords of a circle of lenth 10 cm and 24 cm and distance between them is 17 cm .Find radius

Answer 1

${r }^{2} = {x}^{2} + {12 }^{2} \\ {r}^{2} = (17 - x) {}^{2} + {5}^{2} \\ {x }^{2} + {12}^{2} = (17 - x) {}^{2} + {5}^{2} \\ {x}^{2} + 144 = {17}^{2} - 2(x)(17) + {x}^{2} + 25 \\ 144 = 289 - 34x + 25 \\ 34x = 314 - 144 \\ 34x = 170 \\x = 170 \div 34 \\ x = 5 \\ {r}^{2} = {5}^{2} + 12 {}^{2} \\ {r }^{2} = 25 + 144 \\ {r}^{2} = 169 \\ r = \sqrt{} 169 \\ r = 13$